Class 9

Punjab State Board PSEB 9th Class English Book Solutions English Vocabulary Nature of Words Exercise Questions and Answers, Notes.

PSEB 9th Class English Vocabulary Nature of Words

Read the words and phrases that convey different meanings of the word ‘set given below :

Fixed, started, a group of same things, arranged, written or done, a piece of equipment, put. Now write the word / group of words that give the meaning of ‘set’ against each sentence.

1. My mother gifted a set of handkerchiefs to my younger sister.
2. The jewels were set beautifully in gold.
3. Raghu is well set in his new job.
4. Several TV sets have been stolen from his shop.
5. Let’s start wearing woollen clothes; the winter has set in.
6. The date of the test has not been set yet.
7. She has set the alarm for 5 o’clock, so that she is not late.
8. The surgeon who set my uncle’s hip bone is very popular.
9. Old people have set views about everything.
10. The table has been set for the tea party.
Answer:
1. a group of same things
2. fixed
3. settled
4. a piece of equipment
5. started
6. fixed
7. put fixed
9. fixed
10. arranged.

किसी एक शब्द के विभिन्न प्रयोगों के विभिन्न अर्थ हो सकते हैं। उदाहरण के रूप में नीचे दिए वाक्यों में run शब्द के आथों को देखिए

1. He can run very fast and win the prize. (race)
2. Don’t you think that the film will run at least for 6 weeks? (continue)
3. Suman runs from one table to another to finish her work in time. (hurries)
4. It is strange that Mr. Sahay is able to run two businesses effortlessly. (manages)
5. Our school will run Spoken English classes during the summer vacation. (provide)
6. Trains often run late in winter. (travel)
7. I can’t run on my small salary. (afford)
8. When she peels onions, tears run down her cheeks. (flow)

Punjab State Board PSEB 9th Class English Book Solutions English Grammar Tenses (Concord and Sequence) Exercise Questions and Answers, Notes.

PSEB 9th Class English Grammar Tenses (Concord and Sequence)

Correct the tense in the following sentences :

(a)
1. They have come yesterday.
2. I have bought this house last year.
3. I am the person who have saved your life.
4. I shall call you when the lunch will be ready.
5. Dinesh will come if you will invite him.
6. I had been to Delhi recently.
7. She is one of those persons who never tells a lie.
8. She is working in the office for two years.
9. I had gone to the club last night.
10. I have written to him yesterday.
Answer:
1. They came yesterday.
2. I bought this house last year.
3. I am the person who has saved your life.
4. I shall call you when the lunch is ready.
5. Dinesh will come if you invite him.
6. I have been to Delhi recently.
7. She is one of those persons who never tell a lie.
8. She has been working in the office for two years.
9. I went to the club last night.
10. I wrote to him yesterday.

(b) 1. I hoped that my friend will help me
2. Take care that you will not be cheated.
3. I know them for the last four years.
4. The patient died before the doctor arrived.
5. Newton has discovered the Law of Gravitation.
6. I am studying hard for the last three weeks.
7. He is suffering from fever since Monday.
8. I had visited Shimla last summer.
9. I am sorry I did not write that letter yet.
10. His younger sister is died.
Answer:
1. I hoped that my friend would help me.
2. Take care that you are not cheated.
3. I have been knowing them for the last four years.
4. The patent had died before the doctor arrived.
5. Newton discovered the Law of Gravitation.
6. I have been studying hard for the last three weeks.
7. He has been suffering from fever since Monday.
8. I visited Shimla last summer.
9. I am sorry I have not written that letter yet.
10. His younger sister is dead.

Put the correct Verbs in the blanks :

1. The tallest of these boys ……….. next door to me. (live, lives)
2. Slow and steady ……….. the race. (win, wins)
3. Neither Ashok nor Prem ………. any right to the property. (has, have)
4. Neither the captain nor the soldiers ……….. been arrested. (has, have)
5. Neither he nor I ……….. money to spare for this. (has, have)
6. You, as well as he, ……….. innocent. (is, are)
7. None but the brave ……….. the fair. (deserve, deserves)
8. The United States ……… a prosperous country. (is, are)
9. The committee ………. divided in their opinion. (was, were)
10. I, who ……….. your friend, will stand by you. (is, am, are)
Answer:
1. lives
2. wins
3. has
4. have
5. have
6. are
7. deserves
8. is
9. were
10. am.

Put the correct Verbs in the blanks :

1. All the players in my team ………. done well. (has, have)
2. Bread and butter ……… what they want. (is, are)
3. Either Sushil or Rakesh ……….. done this mischief…….. (has, have)
4. Neither he nor his servants ……….. honest. (was, were)
5. Neither you nor Sham ……….. to be capable of doing this. (appear, appears)
6. Not only the workman but the supervisor also ………. been dismissed. (has, have)
7. Each day and each hour ……….. its own importance. (has, have)
8. The news of the flood ……….. caused great anxiety. (has, have)
9. The jury ……….. divided in their opinion. (was, were)
10. This is one of the best novels that ………… been published this year. (has, have)
Answer:
1. have
2. is
3. has
4. were
5. appears
6. has
7. has
8. has
9. were
10. have.

Put the correct Verbs in the blanks :

1. The cost of all types of pens ………. gone up. (has, have)
2. Time and tide ……….. for none ……….. (wait, waits)
3. Either you or he ……….. mistaken. (is, are)
4. Either Rajinder or his parents ……… responsible for this. (was, were)
5. Neither you nor I ……… lucky. (am, are)
6. He, as well as you, ……….. to blame. (is, are)
7. None of the ships ……….. rescued from the storm. (was, were)
8. The Arabian Nights ……….. interesting stories. (contain, contains)
9. The crew did ……….. best to save the ship. (its, their)
10. This is one of the most difficult lessons that ……… been taught. (has, have)
Answer:
1. has
2. wait
3. is
4. were
5. am
6. is
7. was
8. contains
9. their
10. have.

Put the correct Verbs in the blanks :

1. The toys that were bought by my son……….. really useful. (is, are)
2. Oil and water ……….. mix. (does not, do not)
3. Neither the judge nor the witnesses ……… him. (believe, believes)
4. Neither the Principal nor the lecturers ……….. present at the meeting. (was, were)
5. Either he or I ……….. wrong. (am, are)
6. The workmen, with their leaders ………. been arrested. (have, has)
7. One of my friends ………. the owner of this factory. (is, are)
8. Good crockery ……….. expensive. (is, are)
9. The jury ……….. divided on the issue. (was, were)
10. I am the one who ………. always stood for justice. (has, have)
Answer:
1. are
2. do not
3. believe
4. were
5. am
6. have
7. is
8. is
9. were
10. has.

Put the correct Verb in the blanks :

1. He ……….. regularly. (work, works)
2. Tobacco and alcohol ………. injurious to health. (is, are)
3. Either the officer or the assistants ………. responsible for this error. (is, are)
4. Me or his friends ………. to blame. (was, were)
5. Neither my brother nor I ……….. ever been to Mumbai. (has, have)
6. The gallery, with its beautiful pictures, ………. a great attraction. (is, are)
7. Either of these two proposals ……….. acceptable to me. (is, are)
8. The West Indies ……….. a land of great cricketers. (is, are)
9. The Assembly ……….. in session.
10. He is one of those leaders who …………. always ready to do or die.
Answer:
1. works
2. are
3. are
4. were
5. have
6. is
7. is
8. are
9. is
10. are.

Use Of Tenses

Tense (काल)-Verb के जिस रूप से यह पता चले कि क्रिया कब हुई है, उसे Tense कहा जाता है। Tense तीन प्रकार के होते हैं

1. Present Tense (वर्तमान काल)
2. Past Tense (भूत काल)
3. Future Tense (भविष्य काल)
प्रत्येक Tense के चार भिन्न-भिन्न रूप होते हैं

1. (i) Present Indefinite Tense (or) Simple Present
(ii) Present Continuous Tense
(iii) Present Perfect Tense
(iv) Present Perfect Continuous Tense.

2. (i) Past Indefinite Tense (or) Simple Past
(ii) Past Continuous Tense
(iii) Past Perfect Tense
(iv) Past Perfect Continuous Tense.

3. (i) Future Indefinite (or) Simple Future
(ii) Future Continuous Tense
(iii) Future Perfect Tense
(iv) Future Perfect Continuous Tense.

(A) Present Tense

1. Present Indefinite Tense प्रयोग – इस Tense का प्रयोग निम्नलिखित स्थितियों में किया जाता है
1. सदा सत्य बातों के लिए:
(The sun shines by day, and the moon by night.)

2. चरित्र-सम्बन्धी स्थायी आदतों के लिए –
(He never tells a lie.)

3. वास्तविक Present और निकट भविष्य के लिए –
1. I understand what you say.
2. He leaves for Mumbai tomorrow.

नियम-

• इस Tense में Verb की पहली फार्म का प्रयोग किया जाता है।
• यदि subject एकवचन हो, तो verb की पहली फार्म के साथ या का प्रयोग किया जाता है।
• Negative तथा Interrogative वाक्यों में Helping Verb के रूप में do / does का प्रयोग किया जाता है।
• बहुवचन subject के लिए do का, एकवचन subject के लिए does का प्रयोग किया जाता है। Does के साथ प्रयोग की जाने वाली Verb की पहली फार्म के साथ s या es नहीं लगाया जाता है।
• I तथा you के लिए प्रयोग की जाने वाली Verb की पहली फार्म के साथ s या es नहीं लगाया जाता है। इनके लिए बहुवचन subject की भान्ति केवल Verb की पहली फार्म का ही प्रयोग किया जाता है।

2. Present Continuous Tense प्रयोग-इस Tense का प्रयोग निम्नलिखित स्थितियों में किया जाता है

1. बोलने या लिखने के समय चल रही किसी घटना का वर्णन करने के लिए; जैसे (He is writing a letter:)
2. किसी आदत अथवा व्यवहार का वर्णन करने के लिए भी कभी-कभी इस Tense का प्रयोग किया जाता है; जैसे
(She is working regularly these days.) नियम- इस Tense के वाक्यों में is / am / are लगा कर Verb के ing. वाले रूप का वर्णन किया जाता है।
Subject + is / am / are + Verb का ing वाला रूप + ………….

Note : Present Continuous Tense तथा Present Indefinite Tense के अन्तर को अच्छी प्रकार समझ लेना चाहिए। निम्नलिखित नियम याद रखिए
Present Indefinite Tense — for habitual actions; for universal truths; for actions going to take place in near future.
Present Continuous Tense — for actions in progress at the time of speaking.

3. Present Perfect Tense प्रयोग-इस Tense का प्रयोग अभी-अभी (वर्तमान में) पूरी हुई किसी घटना का वर्णन करने के लिए
किया जाता है। नियम- इस Tense के वाक्यों में has / have लगा कर Verb की तीसरी फार्म का प्रयोग किया जाता है; जैसे
1. She has just finished her work.
2. I have spent all my money on books.

4. Present Perfect Continuous Tense प्रयोग- इस Tense का प्रयोग तब किया जाता है जब कोई क्रिया भूत काल में आरम्भ हुई हो और अब भी चल रही हो; जैसे
1. He has been reading English for two years.
2. They have been reading this book since morning.

नियम-
(1) इस Tense के वाक्यों में has / have + been + V₁-ing + since / for का प्रयोग किया जाता है।
(2) For का प्रयोग तब किया जाता है जब क्रिया के जारी रहने की अवधि (period of time) दी हुई हो; जैसे for fifteen minutes; for half an hour; for a month; for three years ; for a long time.
(3) Since का प्रयोग तब किया जाता है जब क्रिया के आरम्भ होने का निश्चित समय (point of time) दिया हुआ हो; जैसे
since Sunday; since breakfast; since yesterday ; since Diwali; since January 1998; since the first of May.

(B) Past Tense

1. Past Indefinite Tense प्रयोग- इस Tense का प्रयोग तब किया जाता है जब कोई घटना भूत काल में आरम्भ होकर भूत काल में ही समाप्त हो गई हो। (We learnt English at school.)

नियम-
(1) इस Tense के affirmative वाक्यों में Verb की दूसरी फार्म का प्रयोग किया जाता है।
(2) Negative वाक्यों में did not + Verb की पहली फार्म का प्रयोग किया जाता है।
(3) Interrogative वाक्यों में Did + subject + Verb की पहली फार्म का प्रयोग किया जाता है।
(4) Did का प्रयोग करने के बाद सदा Verb की पहली फार्म का ही प्रयोग किया जाता है।

2. Past Continuous Tense प्रयोग – इस Tense का प्रयोग तब किया जाता है जब कोई क्रिया भूतकाल में किसी निश्चित समय पर चल रही हो। (He was writing a letter when I saw him.)
नियम – इस Tense के वाक्यों में was / were लगा कर Verb के ing वाले रूप का प्रयोग किया जाता है।

Note : Past Continuous Tense तथा Past Indefinite Tense के अन्तर को अच्छी प्रकार से समझ लेना चाहिए। निम्नलिखित नियम याद रखिए
Past Indefinite Tense – for completed activity.
Past Continuous Tense – for continuity in past.

3. Past Perfect Tense प्रयोग – इस Tense का प्रयोग तब किया जाता है यदि कोई क्रिया भूतकाल में किसी निश्चित समय (moment) से पहले या किसी निश्चित समय तक पूरी हो चुकी हो।
1. The patient had died before the doctor came.
2. I had finished my work by evening.

नियम – इस Tense में had लगा कर Verb की तीसरी फार्म का प्रयोग किया जाता है।

Note : यदि किसी वाक्य में भूत काल में घटी हुई दो घटनाओं का वर्णन हो, तो उनमें से जो घटना पहले घटी हो उसके लिए Past Perfect Tense का प्रयोग किया जाता है, और जो घटना अपेक्षाकृत बाद में घटी हो उसके लिए Past Indefinite Tense का प्रयोग किया जाता है।

4. Past Perfect Continuous Tense प्रयोग – इस Tense का प्रयोग तब किया जाता है यदि कोई क्रिया भूतकाल में आरम्भ होकर भूतकाल में ही किसी निश्चित समय पर चल रही हो; जैसे(When I reached there at 2 p.m., he had been waiting for me since 1:30 p.m.) नियम – इस Tense के वाक्यों में had + been + V₁-ing + since / for का प्रयोग किया जाता

(C) Future Tense

Future Indefinite Tense

प्रयोग- इस Tense का प्रयोग साधारण रूप में भविष्य में होने वाली किसी घटना का वर्णन करने के लिए किया जाता है; जैसे–
(The post will arrive late. We shall start early.)
नियम – इस Tense के वाक्यों में will / shall लगा कर Verb की पहली फार्म का प्रयोग किया जाता है।
Note : Will और Shall सम्बन्धी प्रयोग के लिए निम्नलिखित नियम ध्यान में रखिए

(1) Assertive वाक्यों में
1. यदि किसी भविष्य की घटना का केवल साधारण रूप से ही वर्णन हो, तो-
First Person के लिए shall का प्रयोग किया जाता है।
Second और Third Persons के लिए will का प्रयोग किया जाता है।

2. यदि वाक्य में किसी भविष्य-सम्बन्धी आदेश (command), प्रण (promise), निश्चय (determination), धमकी (threat) आदि का वर्णन हो, तो First Person के लिए will का प्रयोग किया जाता है।

3. यदि वक्ता अपने किसी भविष्य-सम्बन्धी उद्देश्य (intention) को प्रकट करना
चाहता हो तो वह अपने लिए Will का प्रयोग करेगा। अर्थात् ऐसे वाक्यों में First person के साथ will का प्रयोग किया जाता है।

(2) Interrogative वाक्यों में
1. प्रश्न-वाचक वाक्यों में प्राय: Will I और Shall you का प्रयोग नहीं किया जाता है।
2. Third Person के लिए will अथवा shall किसी का भी प्रयोग किया जा सकता है।
Shall he – भविष्य सम्बन्धी आदेश आदि के लिए।
Will he – भविष्य सम्बन्धी साधारण क्रिया के लिए।

Future Continuous Tense –

प्रयोग-इस Tense का प्रयोग तब किया जाता है जब भविष्य में किसी विशेष समय का वर्णन हो, और कोई क्रिया उस विशेष समय से पहले आरम्भ होकर उसके बाद में पूरी होनी हो; जैसे
(We shall be waiting for you when you get back tomorrow).
नियम – इस Tense के वाक्यों में will / shall के साथ be लगा कर Verb के ing वाले रूप का प्रयोग किया जाता है।

Note :
Future Continuous Tense तथा Future Indefinite Tense के अन्तर को अच्छी तरह से समझ लेना चाहिए। निम्नलिखित नियम याद रखिए
Future Indefinite Tense – for an action which begins at a certain future moment.
Future Continuous Tense – for an action which begins before and finishes after a certain future moment.

3. Future Perfect Tense –
प्रयोग – इस Tense का प्रयोग तब किया जाता है जब कोई क्रिया भविष्य में किसी समय से पहले पूरी होनी हो; जैसे
(I will have finished my homework by evening.)
नियम – इस Tense में will / shall + have लगा कर Verb की तीसरी फार्म का प्रयोग किया जाता है।

4. Future Perfect Continuous Tense प्रयोग – इस Tense का प्रयोग तब किया जाता है यदि क्रिया भविष्य में किसी निश्चित समय (point of time) तक अथवा किसी निश्चित अवधिः (period of time) के लिए जारी रहनी हो; जैसे (By six o’clock I will have been sitting here for ten hours.)
नियम – इस Tense में will / shall + have been लगा कर Verb के ing वाले रूप का प्रयोग किया जाता है।

	Indefinite	Continuous	Perfect	Perfect Continuous
PRESENT PAST FUTURE	write (s) wrote will/shall write	I am/are writing was/were writing I will/shall be writing	has/have written had written will/shall have written	has/have been written had been written will/shall have been written

Miscellaneous Sentences For Practice

Fill in the blanks with the Present Indefinite form of the verbs given in the brackets :

1. He for a walk every day. (go)
2. She …………………….. up early in the morning. (get)
3. The peon ……………… the bell at 9 o’clock. (ring)
4. I ………………. my parents. (obey)
5. We ……………… our teachers. (respect)
6. We ……………………. our prayers in the morning.
7. She …………………….. sweetly. (sing
8. I do not …………………….. sweets. (like)

Fill in the blanks with the Present Continuous form of the verbs given in the brackets :

1. …………… it …………………… today? (rain)
2. ……….. the peon ……. the bell ? (ring)
3. ………… the boys …………..football ? (play)
4. He ……….. a picture. (paint)
5. We ………… our lesson. (learn)
6. She ……………………. not ……………. food. (cook)
7. I ……………………. a letter. (write)
8. You ………. (run)

Fill in the blanks with the Present Perfect form of the verbs given in the brackets :

1. I ….. my homework. (finish)
2. He …………………… first in the class. (stand)
3. …………you …………. your scooter ? (Sell)
4. ………….. she ……. a car? (buy)
5. They ……………………. their enemy. (murder)
6. We ……………………… the match. (win)
7. The peon ………………….. the bell. (ring)
8. We …….. our duty. (do)

Fill in the blanks with the Present Perfect Continuous form of the verbs given in the brackets :

1. It …………….. since morning. (rain)
2. She ………………….. from fever for a week. (suffer)
3. I ………………….. for you for half an hour. (wait)
4. He ……. his brother with money for five years. (help)
5. We ……………………. for a long time. (fight)
6. She ………………… for a job for several months. (look)
7. ……………………. he books from you since 2011? (borrow)
8. she ………………. in this office since 2013? (work)

Fill in the blanks with the Past Indefinite form of the verbs given in the brackets :

1. India ………………….. independence in 1947. (get)
2. He ………………….. government service in 2012. (join)
3. It …………………… heavily last night. (rain)
4. …………………… he …………… you money? (lend)
5. She ……………………. not ……………………. to my proposal. (agree)
6. Why ……………………. he ……………………. angry with you? (become)
7. The teacher ………………….. the student. (punish)
8. He …………………. to go for a walk daily. (use)

Fill in the blanks with the Past Continuous form of the verbs given in the brackets :

1. It ……………. in the morning. (rain)
2. The peon …… ……………. the bell. (ring)
3. Why …………….. she (weep)
4. She ……………………. clothes. (wash)
5. …………………. she …………………… food ? (eat)
6. …………………. the hunter ……………… birds ? (kill)
7. He a novel ………… (read)
8. My grandmother …………………… a story. (tell)

Fill in the blanks with the Past Perfect form of the verbs given in the brackets :

1. He ………………….. a tiger before I reached the forest. (kill)
2. She …………………… a sweater before I bought a new one. (knit)
3. I ……………….. money from my friend before I received my salary. (borrow)
4. The river ………………….. its banks before the dam was built. (overflow)
5. …………….. she …………… a new dress before his father came ? (buy)
6. Why …………………… he …………….. you before you offended him ? (abuse)
7. My uncle …………………… a new house before he retired from service. (build)
8. ……. you in the race before you defeated him in boxing ? (beat)

Fill in the blanks with the Past Perfect Continuous form of the verbs given in the brackets :

1. We in Delhi for ten years. (live)
2. He ……………….. in this office since 2011. (work)
3. She ……………… in this school for ten years. (teach)
4. ……………. your brother for five years ? (look after)
5. Who …………………. you with money all these years ? (help)
6. The farmer …….. the fields for many days. (plough)
7. The teacher …………………… the students for a long time. (guide)
8. They …….. their country for thirty years. (serve)

Fill in the blanks with Future Indefinite form of the verbs given in the brackets :

1. I ………………… to Delhi. (go)
2. We ……………………. you with money. (help)
3. The peon ………. the bell at 9 o’clock. (ring)
4. ………… she……………….. in time ? (come)
5. …………………… he …………………… you his book ? (lend)
6. She ……………………. a rich man. (marry)
7. The train ………………….. in time. (arrive)
8. They …………………… a match tomorrow. (play)

Fill in the blanks with the Future Continuous form of the verbs given in the brackets :

1. She ……………………. a picture. (paint)
2. I ………………….. a new car. (buy)
3. He ……………………. to Delhi tomorrow.
4. They ………………….. their friends. (help)
5. People ………………….. their work. (do)
6. ……………….. she ………………….. food ? (cook)
7. …………………… they …………………. in the river ? (bathe)
8. He ……………………. not ……………………. his friends. (cheat)

Fill in the blanks with the Future Perfect form of the verbs given in the brackets :

1. She …………………… her work in time. (finish)
2. He ………………….. you with money. (help)
3. They ………………… their clothes. (wash)
4. I ………………….. the situation. (handle)
5. She …………………… her promise. (break)
6. He ……………………. you money. (lend)
7. ……….. you English ? (teach)
8. ………………….. they ……………. bravely ? (fight)

Fill in the blanks with the Future Perfect Continuous form of the verbs given in the brackets :

1. It ………………… for two hours. (rain)
2. They …………….. here for many years. (live)
3. She …………………… English since 2008 (learn)
4. He …………………. Mathematics for many years. (teach)
5. …………………. she ………. in this office since 1985 ? (work)
6. He ……………………. you for a long time. (cheat)
7. They ………………….. the poor since 1982. (help)
8. …… she ……………….. food for the whole family for several (cook)

Concord : Subject-Verb Agreement

1. क्रिया का प्रयोग अवश्य ही इसके कर्ता के अनुसार होना चाहिए।
2. एकवचन कर्ता के साथ एकवचन क्रिया का प्रयोग किया जाता है और बहुवचन कर्ता के साथ बहुवचन क्रिया का प्रयोग किया जाता है।

Singular Subject – Singular Verb	Plural Subject – Plural Verb
This child is very clever. That book was interesting. He has many storybooks. He does not work regularly.	These children are very clever. Those books were interesting. They have many storybooks. They do not work regularly.

याद रखें – I के साथ am, was, have तथा you के साथ are, were, have का प्रयोग किया जाता है।

I am / was angry with him.
I have a good English dictionary.
You are / were late for school.
You have a good house.

3. निम्नलिखित क्रियाओं को negative और question form में बदलने के लिए have का प्रयोग किया जाता है, न कि has का –

do, does, did,
will, would, shall, should,
can, could, may, might,
must, need, dare,
ought to, used to
Examples :

• Does she have a new frock ?
• We do not have a high school in our village.
• Did he have his share ?
• I shall have a lot of money next week.
• He used to have a car.
• Mohan must have finished his work.

कुछ वाक्यों में ‘There’ कर्ता का स्थान ले लेता है। वास्तविक कर्ता क्रिया के बाद आता है।

• There is a table in this room.
• There are ten desks in this room.
• There was a clock on the wall.
• There were pictures on the wall.
• There has been a mistake.
• There have been many mistakes.

याद रखिए कि ऐसे वाक्यों में क्रिया वास्तविक कर्ता के अनुसार होती है। यदि वास्तविक कर्ता एकवचन (a table, a clock, a mistake) हो तो क्रिया भी एकवचन (is, was, has) होती है। यदि वास्तविक कर्ता बहुवचन (ten desks, pictures, many mistakes) हो तो क्रिया भी बहुवचन (are, were, have) होती है। परन्तु ‘There’ के विपरीत It’ के साथ सदा एकवचन क्रिया का प्रयोग किया जाता है।

• It is hot today.
• It was 7:30 at that time.
• It has been a mistake.

प्रायः हम एक भूल कर जाते हैं, जिसे “Error of Proximity” कहा जाता है, हम क्रिया को इसके साथ लगती संज्ञा की मात्रा के अनुसार कर देते हैं। निम्नलिखित उदाहरणों में दिखाए अनुसार हमें इनसे बचना चाहिए।

• The quality of the mangoes was (not ‘were) not good.
• His knowledge of Indian vernaculars is (not are) very sound.
• The state of his affairs was (not ‘were) such as to cause anxiety to his parents.
• The results of the new policy are (not is) very encouraging.

4. and’ द्वारा जोड़े गए दो या दो से अधिक एकवचन संज्ञाओं या सर्वनामों के साथ बहुवचन क्रिया का प्रयोग किया जाता है। जैसे –

• Gold and silver are precious metals.
• Fire and water do not agree.
• Are your father and mother at home ?
• He and I were playing.

परन्तु यदि संज्ञाएं हमारे दिमाग को एक विचार देती हैं, अथवा किसी एक ही व्यक्ति अथवा वस्तु की ओर संकेत करती हैं, तो एकवचन क्रिया का प्रयोग किया जाता है। जैसे –

• The horse and carriage is at the door.
• Bread and butter is his only food.
• Honour and glory is his reward.
• The novelist and poet is dead.

5. एकवचन के साथ with, as well as, आदि द्वारा जोड़े गए शब्द उपवाक्य सम्बन्धी होते हैं। इसलिए एकवचन क्रिया का प्रयोग किया जाना चाहिए; जैसे –

• The house, with its contents, was insured.
• The Chairman, with the directors, is to be present.
• The ship, with its crew, was lost.
• Silver, as well as cotton, has fallen in price.
• Sanskrit, as well as Arabic, was taught there.
• Justice, as well as mercy, allows it.

6. or अथवा nor द्वारा जोड़े गए दो या दो से अधिक कर्ताओं के साथ एकवचन क्रिया का प्रयोग किया जाता है। जैसे –

• No nook or corner was left unexplored.
• Our happiness or our sorrow is largely due to our own actions.
• Either the cat or the dog has been here.
• Neither food nor water was to be found there.
• Neither praise nor blame seems to affect him.

7. जब or अथवा nor द्वारा जोड़े गए कर्ताओं में से एक बहुवचन हो, तब क्रिया भी बहुवचन होनी चाहिए, और बहुवचन कर्ता को क्रिया के समीपतम् रखना चाहिए; जैसे –
Neither the chairman nor the directors are present. जब or अथवा nor द्वारा जोड़े गए कर्ता अलग-अलग सर्वनामों से सम्बन्धित हों तो क्रिया समीपतम् सर्वनाम के अनुसार होनी चाहिए; जैसे –

• Either he or I am mistaken
• Either you or he is mistaken.
• Neither you nor he is to blame.
• Neither my friend nor I am to blame.

Either, neither, each, everyone, many a के साथ एकवचन क्रिया का प्रयोग किया जाना चाहिए; जैसे

• He asked me whether either of the applicants was suitable.
• Neither of the two men was very strong.
• Each of these minerals is found in India.
• Everyone of the boys loves to ride.
• Many a man has done so.

ऐसी दो संज्ञाएं जिनसे पूर्व each अथवा every लगा हो और वे and द्वारा जुड़ी हुई हों, तो ऐसी स्थिति में उनके साथ एकवचन क्रिया का प्रयोग किया जाता है जैसे –

• Each boy and each girl was present in the class.
• Every table and every chair has been dusted.

8. कुछ संज्ञाएं जिनका रूप बहुवचन में होता है, परन्तु जिनका अर्थ एकवचन में होता है, ऐसी संज्ञाओं के साथ एकवचन क्रिया का प्रयोग किया जाता है; जैसे –

• The news is true.
• Politics was with him the business of his life.
• The wages of sin is death.
• Mathematics is a branch of study in every school.

कुछ संज्ञाएं जिनका रूप एकवचन में होता है, परन्तु जिनका अर्थ बहुवचन में होता है, ऐसी संज्ञाओं के साथ बहुवचन क्रिया का प्रयोग किया जाता है; जैसे – Twelve dozen cost one hundred rupees.

9. किसी समूह-वाचक संज्ञा के साथ एकवचन क्रिया का प्रयोग होता है जब उस समूह को समूचे पूर्णांक के रूप में ले लिया जाए; और बहुवचन क्रिया का प्रयोग तब होता है जब उसी समूह को उसकी विभिन्न इकाइयों के रूप में लिया जाए; जैसे –
1. The committee has issued its report.
2. The committee are divided on one minor point.
परन्तु हमें समरूप होना चाहिए। इस प्रकार, हमें कहना चाहिए :
The committee has appended a note to its (not their) report.

10. जब कोई बहुवचन संज्ञा किसी एक वस्तु अथवा किसी सामूहिक इकाई का एक विशेष नाम हो, तब इसके साथ एकवचन क्रिया का प्रयोग किया जाना चाहिए; जैसे –

• The Arabian Nights is still a great favourite.
• The United States has a big navy.
• Plutarch’s Lives is an interesting book.
• Gulliver’s Travels was written by Swift.

11. जब कोई बहुवचन संज्ञा किसी ऐसी विशेष संख्या अथवा मात्रा की ओर संकेत करती है जिसे एक समूचा पूर्णांक माना गया हो, तब क्रिया प्रायः एकवचन होती है; जैसे –

• One hundred paise is equal to one rupee.
• Six miles is a long distance.
• Fifty thousand rupees is a large sum.
• Three parts of the business is left for me to do.

Complete these sentences with one of the two verbs given in brackets :

1. They ……….. going to report the matter to the Principal. (is / are)
2. She ………… not have any chance of winning the election. (do / does)
3. The teacher does not ……….. much work to do. (has / have)
4. ……….. you have any money with you ? (Do / Does)
5. Doesn’t Chennai ……….. a severe winter ? (has / have)
6. ………… the men shouting loudly ? (Was / Were)
7. Can we ………… coffee instead of tea ? (has / have)
8. Don’t the students ……………. their books with them ? (has / have)
9. ……………. your friend visit you daily ? (Do / Does)
10. They needn’t …………… gone there so early. (has / have)
Answer:
1. are
2. does
3. have
4. Do
5. have
6. Were
7. have
8. have
9. Does
10. have.

Choose the correct verb out of the two given in brackets and rewrite the sentences :

1. The cause of both the accidents (was, were) the same.
2. Each of the boys (has, have) done his homework.
3. All my friends (has, have) joined this college.
4. (Have, has) either of you any money?
5. Everyone of us (is, are) going to the film.
6. Both the rooms (was, were) whitewashed…
7. One of the debators (was, were) very interesting.
8. The furniture (is, are) to be sold today.
9. A few sheep (was, were) running about in the field.
10. Neither Manu nor Misha (was, were) with us today.
Answer:
1. was
2. has
3. have
4. Has
5. is
6. were
7. was
8. is
9. were
10. was.

Sequence Of Tenses

यदि मुख्य-वाक्य की क्रिया Present Tense में हो, तो उपवाक्य की क्रिया किसी भी Tense में हो सकती है; जैसे

1. He assures me that the train has arrived.
2. He says she will come at 4 p.m.
3. The Principal declares that latecomers will be fined.
4. Subhash says that they had been sitting there for two hours.
5. The witness affirms that the accused is not guilty.

2. यदि मुख्य वाक्य की क्रिया Future Tense में हो, तो उप-वाक्य की क्रिया किसी भी Tense में हो सकती है; जैसे
1. He will assure me that the train has arrived.
2. He will assure me that the train had arrived.
3. He will say that Ramesh is late.
4. He will say that Ramesh was late.
5. He will tell us that Radha is waiting for us at the bus stop.

3. यदि मुख्य-वाक्य की क्रिया Past Tense में हो, तो उप-वाक्य की क्रिया भी Past Tense में ही होनी चाहिए। (किन्तु यदि उप-वाक्य में किसी Habit या Universal truth का वर्णन हो, तो इसकी क्रिया Present Tense में ही रहती है।)
1. He assured me that the train had arrived.
2. She said that she would come at 4 p.m.
3. The Principal declared that latecomers would be fined.
4. He told me that he never tells a lie.
5. The teacher said that honesty is the best policy.

If Patterns

(If से आरम्भ होने वाले उप-वाक्य) नीचे दिए गए चार्ट को सदा ध्यान में रखिए- ‘.

If Clause	Main Clause
I   Form II   Form Had + III Form	will + I Form would + I Form would have + III Form

नोट : Until और unless से आरम्भ होने वाले उप-वाक्यों में भी यही नियम लागू होते हैं।
Examples :
1. If you play the piano, I will sing.
If you played the piano, I would sing.
If you had played the piano, I would have sung.

2. He will beat the thief if he catches him.
He would beat the thief if he caught him.
He would have beaten the thief if he had caught him.

3. The horse will kick you if you go near it.
The horse would kick you if you went near it.
The horse would have kicked you if you had gone near it.

4. He will not play tennis if you do not give him a racket.
He would not play tennis if you did not give him a racket.
He would not have played tennis if you had not given him a racket.

5. He will walk to the station if he is well.
He would walk to the station if he was well.
He would have walked to the station if he had been well.

6. My servant can paint your boat if you give him a brush.
My servant could paint your boat if you gave him a brush.
My servant could have painted your boat if you had given him a brush.

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 9 Areas of Parallelograms and Triangles Ex 9.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.1

Question 1.
Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and the two parallels.

(i)

Answer:
In figure (i), trapezium ABCD and ∆ PDC lie on the same base and between the same parallels.
Here, DC is the common base and DC and AB are two parallels.

(ii)

Answer:
In figure (ii), no two figures lie on the same base and between the same parallels.

(iii)

Answer:
In figure (iii), parallelogram PQRS and ∆ TQR lie on the same base and between the same parallels.
Here, QR is the common base and QR and PS are two parallels.

(iv)

Answer:
In figure (iv), no two figures lie on the same base and between the same parallels.

(v)

Answer:
In figure (v), parallelograms ABCD and APQD as well as trapeziums ABQD and APCD, all the four figures, lie on the same base and between the same parallels.
Here, AD is the common base and AD and BQ are two parallels.

(vi)

Answer:
In figure (vi), no two figure lie on the same base and between the same parallels.

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 8 Quadrilaterals MCQ Questions with Answers.

PSEB 9th Class Maths Chapter 8 Quadrilaterals MCQ Questions

Multiple Choice Questions and Answer

Answer each question by selecting the proper alternative from those given below each question to make the statement true:

Question 1.
The ratio of four angles in order of a quadrilateral is 2 : 4 : 5 : 4. Then, the measure of the smallest angle of the quadrilateral is
A. 120°
B. 96°
C. 48°
D. 60°
Answer:
C. 48°

Question 2.
In quadrilateral PQRS, ∠P = 5x, ∠Q = 3x, ∠R = 4x and ∠S = 6x. Then, the measure of the greatest angle of quadrilateral PQRS is …………… .
A. 100°
B. 60°
C. 80°
D. 120°
Answer:
D. 120°

Question 3.
In quadrilateral ABCD, ∠A + ∠B = 150°.
Then ∠C + ∠D =
A. 105°
B. 210°
C. 150°
D. 300°
Answer:
B. 210°

Question 4.
In trapezium PQRS, PQ || RS. If ∠P = 150°, then ∠S = …………. .
A. 75°
B. 150°
C. 60°
D. 30°
Answer:
D. 30°

Question 5.
The perimeter of parallelogram ABCD is 22 cm.
If AB = 4 cm, then BC = ……………. cm.
A. 7
B. 6
C. 5.5
D. 4
Answer:
A. 7

Question 6.
In parallelogram ABCD, ∠A – ∠B = 30°. Then, ∠C = ……………… .
A. 105°
B. 75°
C. 150°
D. 60°
Answer:
A. 105°

Question 7.
In parallelogram ABCD, the bisectors of ∠A and ∠B intersect at M. If ∠A = 80°, then ∠AMB = ……………. .
A. 40°
B. 50°
C. 80°
D. 90°
Answer:
D. 90°

Question 8.
In parallelogram ABCD, the ratio ∠A : ∠B : ∠C : ∠D can be
A. 3 : 4 : 5 : 6
B. 2 : 3 : 3 : 2
C. 2 : 3 : 2 : 3
D. 2 : 3 : 5 : 8
Answer:
C. 2 : 3 : 2 : 3

Question 9.
In parallelogram ABCD, 3 ∠ A = 2 ∠ B. Then, ∠ D = ………………. .
A. 120°
B. 108°
C. 72°
D. 60°
Answer:
B. 108°

Question 10.
In ∆ ABC, E and F are the midpoints of AB and AC respectively. If EF = 4 cm, then BC = …………… cm.
A. 8
B. 2
C. 4
D. 12
Answer:
A. 8

Question 11.
In ∆ ABC, P is the midpoint of AB and Q is the midpoint of AC. Then, PQCB is a ………….. .
A. trapezium
B. parallelogram
C. rectangle
D. rhombus
Answer:
A. trapezium

Question 12.
In ∆ ABC, D, E and F are the midpoints of AB, BC and CA respectively. If the perimeter of ∆ DEF is 30 cm, then the perimeter of ∆ ABC is ……………. cm.
A. 15
B. 30
C. 45
D. 60
Answer:
D. 60

Question 13.
∆ ABC is an equilateral triangle. D, E and F are the midpoints of AB, BC and CA respectively. If AB = 8 cm, the perimeter of ∆ DEF is …………… cm.
A. 24
B. 12
C. 6
D. 48
Answer:
B. 12

Question 14.
ABCD is a rectangle. If AB = 5 cm and BC = 12
cm, then BD = ………………. cm
A. 17
B. 13
C. 8.5
D. 1
Answer:
B. 13

Question 15.
ABCD is a rhombus. If AC = 10 cm and BD = 24 cm, the perimeter of ABCD is …………………. cm.
A. 13
B. 26
C. 52
D. 48
Answer:
C. 52

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 8 Quadrilaterals Ex 8.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 8 Quadrilaterals Ex 8.2

Question 1.
ABCD is a quadrilateral in which F Q, R and S are midpoints of the sides AB, BC, CD and DA respectively (see the given figure 1). AC is a diagonal. Show that:
(i) SR || AC and SR = \(\frac{1}{2}\) AC
(ii) PQ = SR
(iii) PQRS is a parallelogram.

Answer:
In ∆ DAC, S and R are the midpoints of DA and DC respectively.
Through C draw a line parallel to AD which intersects line SR at T.
In ∆ DRS and ∆ CRT
∠ DRS = ∠ CRT (Vertically opposite angles)
∠ RSD = ∠ RTC (Alternate angles formed by transversal ST of DS || TC)
DR = CR (R is the midpoint of DC.)
∴ ∆ DRS ≅ ∆ CRT (AAS rule)
∴ DS = CT and SR = RT (CPCT)
As S is the midpoint of DA, we have DS = SA.
∴ SA = CT
And, by construction, SA || CT.
∴ Quadrilateral SACT is a parallelogram.
∴ ST || AC
∴ SR || AC ………… (1)
Now, SR = RT gives SR = \(\frac{1}{2}\)ST
In parallelogram SACT, ST = AC.
∴ SR = \(\frac{1}{2}\)AC ……………. (2)
Taking (1) and (2) together,
SR || AC and SR = \(\frac{1}{2}\)AC ….. Result (1)
Similarly, in ∆ ABC, P and Q are the midpoints of AB and BC respectively. ,
∴ PQ || AC and PQ = \(\frac{1}{2}\)AC
Now, SR = \(\frac{1}{2}\)AC and PQ = \(\frac{1}{2}\)AC
∴ PQ = SR …… Result (ii)
Similarly, SR || AC and PQ || AC.
∴ PQ || SR
Thus, in quadrilateral PQRS, PQ = SR and PQ || SR.
Hence, by theorem 8.8, PQRS is a parallelogram. … Result (iii)

Question 2.
ABCD is a rhombus and F Q, R and S are the midpoints of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.
Answer:

ABCD is a rhombus and F Q, R and S are the midpoints of sides AB, BC, CD and DA respectively.
∴ In ∆ ABC, PQ || AC and PQ = \(\frac{1}{2}\)AC.
∴ In ∆ ADC, SR || AC and SR = \(\frac{1}{2}\)AC.
Hence, in quadrilateral PQRS, PQ || SR and PQ = SR.
∴ Quadrilateral PQRS is a parallelogram.
Now, since ABCD is a rhombus, AC and BD bisect each other at right angles at M.
∴ ∠ AMB = 90°
Now, AC || PQ and MN is their transversal.
∴ ∠ AMN + ∠ MNP = 180° (Interior angles on the same side of transversal)
∴ ∠ AMB + ∠MNP = 180°
∴ 90° + ∠ MNP = 180°
∴ ∠ MNP = 90°
In ∆ ABD, P and S are the midpoints of AB and AD respectively.
∴ PS || BD and NP is their transversal.
∴ ∠ DNP + ∠ NPS = 180°
∴ ∠ MNP + ∠ NPS =180°
∴ 90° + ∠ NPS = 180°
∴ ∠ NPS = 90°
∴ ∠ SPQ = 90°
Thus, in parallelogram PQRS, one angle ∠P is a right angle.
Hence, quadrilateral PQRS is a rectangle.

Question 3.
ABCD is a rectangle and P, Q, R and S are midpoints of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.
Answer:

Since ABCD is a rectangle, its diagonals are equal.
∴ AC = BD
∴ \(\frac{1}{2}\)AC = \(\frac{1}{2}\)BD
In ∆ ABC, P and Q are the midpoints of AB and BC respectively.
∴ PQ = \(\frac{1}{2}\)AC
Similarly, in ∆ ADC, SR = \(\frac{1}{2}\)AC; in ∆ ABD, SP = \(\frac{1}{2}\) BD and in ∆ BCD, QR = \(\frac{1}{2}\) BD.
Now, PQ = SR = \(\frac{1}{2}\)AC, SP = QR = \(\frac{1}{2}\)BD and \(\frac{1}{2}\)AC = \(\frac{1}{2}\)BD
Hence, in quadrilateral PQRS,
PQ = QR = RS = SP
Thus, all the sides of quadrilateral PQRS are equal.
Hence, quadrilateral PQRS is a rhombus.

Question 4.
ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the midpoint of AD. A line is drawn through E parallel to AB intersecting BC at F (see the given figure). Show that F is the midpoint of BC.

Answer:
Suppose line EF drawn through E and parallel to AB intersects BD at M.
EF || AB and AB || DC
∴ EF || DC
Trapezium ABCD is divided into two triangles, ∆ ABD and ∆ BCD, by diagonal BD.
In ∆ ABD, E is the midpoint of AD and a line through E and parallel to AB intersects BD at M.
Hence, by theorem 8.10, M is the midpoint of BD.
Now, in ∆ BCD, M is the midpoint of BD and a line through M and parallel to CD intersects BC at F.
Hence, by theorem 8.10, F is the midpoint of BC.
Note: The following result about the length of EF can also be derived:
EF = \(\frac{1}{2}\)(AB + CD)
Moreover, if X and Y are the midpoints of the diagonals of above trapezium ABCD, then XY = \(\frac{1}{2}\)|AB – CD|.

Question 5.
In a parallelogram ABCD, E and F are the midpoints of sides AB and CD respectively (see the given figure). Show that the line segments AF and EC trisect the diagonal BD.

Answer:
E and F are the midpoints of AB and CD respectively.
∴ AE = \(\frac{1}{2}\)AB and CF = \(\frac{1}{2}\)CD
In parallelogram ABCD, AB = CD and AB || CD.
∴ AE = CF and AE || CF
Hence, quadrilateral AECF is a parallelogram.
∴ AF || EC
∴ AP || EQ
In ∆ ABP E is the midpoint of AB and EQ || AR
∴ Q is the midpoint of PB. (Theorem 8.10)
∴PQ = QB …………… (1)
Similarly, in ∆ DQC, F is the midpoint of DC and FP || CQ.
∴ P is the midpoint of DQ. (Theorem 8.10)
∴ DP = PQ …………….. (2)
From (1) and (2), DP = PQ = QB.
Moreover, DP + PQ + QB = BD.
Thus, AF and EC trisect the diagonal BD.

Question 6.
Show that the line segments joining the midpoints of the opposite sides of a quadrilateral bisect each other.
Answer:

In quadrilateral ABCD, P Q, R and S are the midpoints of sides AB, BC, CD and DA respectively.
In ∆ ABC, P and Q are the midpoints of AB and BC respectively.
∴ PQ || AC and PQ = \(\frac{1}{2}\)AC …………….. (1)
In ∆ ADC, S and R are the midpoints of DA and DC respectively.
∴ SR || AC and SR = \(\frac{1}{2}\)AC ……………… (2)
From (1) and (2),
PQ = SR and PQ || SR.
Thus, in quadrilateral PQRS, sides in one pair of opposite sides are equal and parallel. Hence, quadrilateral PQRS is a parallelogram. The diagonals of a parallelogram bisect each other. [Theorem 8.6]
∴ PR and SQ bisect each other.
Thus, the line segments joining the midpoints of the opposite sides of a quadrilateral bisect each other.

Question 7.
ABC is a triangle right angled at C. A line through the midpoint M of hypotenuse AB and parallel to BC intersects AC at D. Show that:
(i) D is the midpoint of AC.
(ii) MD ⊥ AC
(iii) CM = MA = \(\frac{1}{2}\)AB
Answer:

In ∆ ABC, ∠ C is a right angle and M is the midpoint of hypotenuse AB. A line through M and parallel to BC intersects AC at D.
Hence, by theorem 8.10, DM bisects AC.
∴ D is the midpoint of AC. ….. Result (i)
In ∆ ABC, ∠ C is a right angle.
∴ ∠ C = 90°
Now, BC || DM and DC is their transversal.
∴ ∠ MDC + ∠ DCB = 180° (Interior angles on the same side of transversal)
∴ ∠ MDC + 90° = 180°
∴ ∠ MDC = 90°
Thus, MD is perpendicular to AC.
∴ MD ⊥ AC …… Result (ii)
Now, in ∆ ADM and ∆ CDM,
AD = CD (D is the midpoint of AC)
∠ ADM = ∠ CDM (Right angles)
DM = DM (Common)
∴ ∆ ADM ≅ ∆ CDM (SAS rule)
∴ AM = CM (CPCT) ……………. (1)
Now, M is the midpoint of AB.
∴ AM = \(\frac{1}{2}\)AB …… (2)
< Prom (1) and (2),
CM = MA = \(\frac{1}{2}\)AB …… Result (iii)

Punjab State Board PSEB 9th Class English Book Solutions English Grammar Non-Finites Exercise Questions and Answers, Notes.

PSEB 9th Class English Grammar Non-Finites

(a) Fill up the blanks, selecting suitable to-infinitives from the following list :

(to see, to implement, to do, to announce, to show, to join, to let, to waste, to play, to do, to go, to solve, to post, to ask, to remember)

1. It is time ………………
2. That was a sight …..
3. The judge has a judgement ………
4. That is something ………………..
5. I have a new plan ……………
6. I have a nice picture ……….
7. Have you any plan ……………… the college ?
8. I have some questions ……………… you.
9. Have you any work ……………. ?
10. I have a house 11. She has no problem ………………
12. I have no time …………….
13. Do you have any letters …………..
14. He has some homework …………..
15. Bedi has a match ……………… on Sunday.
Answer:
1. to go
2. to see
3. to announce
4. to remember
5. to implement
6. to show
7. to join
8. to ask
9. to do
10. to let
11. to solve
12. to waste
13. to post
14. to do
15. to play.

(b) Frame seven meaningful sentences from the table below :

I have

some letters some homework some good news a question some pictures a match no time

to ask you to waste to play on Sunday to show you to do to tell you to post

1. I have some letters to post.
2. I have some homework to do.
3. I have some good news to tell you.
4. I have a question to ask you.
5. I have some pictures to show you.
6. I have a match to play on Sunday.
7. I have no time to waste.

Fill up the blanks with the Present Participle form of the following Verbs :

(a) (smoke, look, spit, swim, read, wait, go, read, eat, see)

1. …………… is a very good exercise.
2. No …………….. in this compartment.
3. ……………. French is easier than to speak it.
4. ………….. after children requires patience.
5. ………….. between meals is bad.
6. No ……………….
7. He insisted on ……………. her.
8. I am quite used to ……………… in queues.
9. Do you feel like …………….. for a swim ?
10. I am looking forward to ……………… that book.
Answer:
1. Swimming
2. smoking
3. Reading
4. Looking
5. Eating
6. spitting
7. seeing
8. waiting
9. going
10. reading.

(b) (travel, talk, work, walk, ride, see, wait, steal, drop, smoke, cut)

1. He is used to …………….. at night.
2. Try to avoid ……………. in the rush hour.
3. There’s nothing here worth ………….
4. Stop ……..
5. Would you mind ……………… a moment ?
6. He prefers …………….. to …………
7. The grass needs …………..
8. I don’t allow ……………… here.
9. I heard the cork ………..
10. I caught him ……………… my apples.
Answer:
1. working
2. travelling
3. seeing
4. talking
5. waiting
6. walking, riding
7. cutting
8. smoking
9. dropping
10. stealing.

Put the – ing forms (Participles) of the following Verbs in the blanks in the following sentences :

(please, write, rise, run, tire, drip, bore, work, grow, amuse.)
1. I caught a …………….. dog.
2. It was a ……………… sight.
3. We had a …………….. journey.
4. Give him a …………… pad.
5. …………… crops need care.
6. I do not like ……………… taps.
7. Did you see the …………….. flames ?
8. It was a ……………….. play.
9. We had an ……………… talk.
10. The government is looking after the …………… classes.
Answer:
1. running
2. pleasing
3. tiring
4. writing
5. Growing
6. dripping
7. rising
8. boring
9. amusing
10. working.

Given below are some pairs of sentences. Combine them into single sentences, using the Participle Phrases :

1. I saw a thief.
He was running away towards the station.

2. You can see the child.
She is sleeping peacefully.

3. His brother came home.
He brought an English wife with him.

4. Kindly give something to the poor beggar.
He is crying for alms.

5. The prince slept soundly.
He dreamt of his bright future.

6. My father came back home.
He brought some fruit for use.

7. Ram killed the witness.
He was giving a statement.

8. A police officer came to my house today.
He brought my missing bicycle with him.

9. I can hear my son.
He is saying prayers.

10. Could you bring me a pen ?
It is lying on the shelf.
Answers
1. I saw a thief running away towards the station.
2. You can see the child sleeping peacefully.
3. His brother came home bringing an English wife with him.
4. Kindly give something to the poor crying beggar.
5. The prince slept soundly dreaming of his bright future.
6. My father came back home bringing some fruit for use.
7. Ram killed the witness giving a statement.
8. A police officer came to my house today bringing my missing bicycle with him.
9. I can hear my son saying prayers.
10. Could you bring me a pen lying on the shelf?

Fill in the blanks with correct Past Participle form of the given verbs :

(wound, cook, burn, break, write, build, rot, lose, unlock, fade, close, paint, translate, finish, fail)

1. I got my house ……………
2. He got the book …………
3. The …………… soldier was taken to the hospital.
4. The overseer is getting this house ……..
5. The ……………… rose was thrown out.
6. You must get the room ……………..
7. The …………….. food got spoilt.
8. Give a ……………… statement.
9. A ……………. child dreads the fire.
10. This college does not admit ……….. students.
11. He died of a …………….. heart.
12. The officer wants this work ………….. by today.
13. Who likes ……………. vegetables ?
14. That lady found her ……………… purse.
15. I found all the doors
Answer:
1. built
2. translated
3. wounded
4. unlocked
5. faded
6. painted
7. cooked
8. written
9. burnt
10. failed
11. broken
12. finished
13. rotten
14. lost
15. closed.

Combine the following sentences, using Participles or Gerunds or Infinitives :

1. I made a journey to Mumbai yesterday. I went there to get the best financial advice.
2. Your parcel never reached me. It had been addressed to the wrong place.
3. Turn to the right. You will find the office.
4. He drew his sword. He rushed at the king.
5. It was my purse. It had been lost.
6. He made a promise. He kept it also.
7. One must serve twenty years. After that one can retire.
8. He said he would come today. I was pleased at this.
9. I promise to help you in time of need. You can rely on this.
10. She was praised by all. She grew proud.
Answer:
1. I made a journey to Mumbai to get the best financial advice.
2. Having been addressed to the wrong place, your parcel never reached me.
3. Turning to the right, you will find the office.
4. Drawing his sword he rushed at the king.
5. It was my lost purse.
6. Having made a promise he kept it also.
7. After serving for twenty years one can retire.
8. I was pleased to hear of his coming today.
9. You can rely on my promise to help you in times of need.
10. Being praised by all, she grew proud.

The Infinitive

क्रिया के मूल रूप को Infinitive कहा जाता है। इस पर कर्ता के Number और Person का कोई प्रभाव नहीं होता है।
Infinitive दो प्रकार के होते हैं :
Bare Infinitive : यह क्रिया का वह मूल रूप होता है जिसके साथ to नहीं लगता है।
I saw her weep. — We made her sing.

To-Infinitive : यह क्रिया का वह मूल रूप होता है जिसके साथ to लगा होता है।
I want to go now. — We have to pay taxes.

The Use of Bare-Infinitive

Bare-Infinitive का प्रयोग निम्नलिखित हालतों में किया जाता है :

1. निम्नलिखित सहायक क्रथाओ के बाद
do, does, did, can, could, will, would, shall, should, may, might, need, must, dare.
1. I shall accompany you.
2. He may come today.
3. You need not do it.

2. निम्नलिखित सकर्मत (Transitive) कियाओं के बाद :

make, let, bid, feel, hear, see, watch, notice, observe, if I
1. ‘I heard him go up the stairs.
2. I saw him steal my pen.
3. I felt the cold air strike against my face.
4. He made her weep every day.

3. had और would वाले निम्नालिखित phrases के बाद :

had better, had rather, would rather, had sooner, would sooner.
1. I would rather die than beg.
2. You had better stop smoking.

4. than (conjunction) it but (preposition) etc are :

1. I would rather walk than ride your scooter.
2. He did nothing but laugh.
नोट : but के बाद ‘bare-infinitive’ का प्रयोग केवल तभी किया जाता है जब but से पूर्व मुख्य क्रिया के रूप में do, does, did का प्रयोग किया गया हो।

The Use of To-Infinitive.

To-infinitive का प्रयोग निम्नलिखित हालतों में किया जाता है :

1. ought और have के साथ to-infinitive का प्रयोग किया जाता है यदि इन शब्दों का प्रयोग किसी जिम्मेदारी (obligation) अथवा कर्त्तव्य को प्रकट करने के लिए किया गया हो।

1. You ought to respect your elders.
2. We ought to help the poor.
3. I have to support my family.
4. She has to live with her parents.
5. Boys had to pay their fees.

2. किसी कारण अथवा उद्देश्या के प्रकट करने के लिए भी to-invinitive का प्रयोग किया जाता ह

1. She came here to consult you.
2. I went to Delhi to meet my brother.
3. They stopped at the market to buy some apples.
4. We did not go there to earn money.

निम्नलिखित क्रियाओं के साथ to-infinitive लगाया जाता है यदि उनका प्रयोग किसी मनोरथ, इच्छा अथवा तत्परता को प्रकट करने के लिए किया गया हो :

want, hope, like, love, hate, promise, intend, propose, decide, swear, learn, remember, forget, agree, consent, neglect, refuse, attempt, fail, hesitate, prepare, care, pretend, determine, arrange, seem.
1. I want to go now.
2. She decided to marry him.
3. I forgot to answer this question.
4. They promised to pay all the taxes.

निम्नलिखित सकर्मक क्रियाओं के साथ कर्म (object) लगाने के बाद to-infinitive का प्रयोग किया जाता है :

ask, advise, allow, beg, compel, courage, force, instruct, invite, order, permit, request, tell, teach, warn, Bici
1. I begged him to help me.
2. My mother asked me to work hard.
3. The teacher allowed him to go.
4. The boys requested the teacher to forgive them.

Fill in the blanks with the correct form of the verbs given in brackets :

1. Mohan wants ………………. (swim) in the river.
2. The teacher asked him ……………….. (get) out of the room.
3. I forgot ……………….. (bring) my purse.
4. Let him ……………….. (go) now.
5. I have come ……………….. (see) the Principal.
6. It began ……………….. (rain) and we couldn’t go out.
7. We saw him ……………. (arrive) at the station.
8. The book was easy …………….. (read).
9. We didn’t expect Ram …………. (win).
10. They heard her ………………. (sing) a sweet song.
11. Mohan knows how ……………….. (answer) this question.
12. He was too tired ……………….. (walk).
13. He made me …………….. (do) it.
14. They stopped ……………… (have) some rest.
15. He is saving money ………….. (buy) a scooter.
16. Would you like …….. (have) dinner with us?

The Gerund

-ing प्रत्यय वाली ऐसी क्रिया जो Noun का काम कर रही हो उसे Gerund कहा जाता है। इसका प्रयोग निम्नलिखित स्थितियों में किया जा सकता है :

1. Subject to a Verb	1. Swimming improves one’s health. 2. Smoking causes cancer.
2. Object to a Verb	1. I dislike smoking. 2. I love swimming.
3. Object to a Preposition	1. He is fond of playing. 2. She was fined for coming late.
4. Complement to a Linking Verb	1. His only aim was cheating. 2. My favourite hobby is gardening.
5. In apposition to a Pronoun	1. It is no use crying. 2. It is foolish saying that.

Gerunds के प्रयोग के सम्बन्ध में ध्यान रखने योग्य बातें :

1. निम्नलिखित क्रियाओं के साथ कर्म (object) के रूप में to-infinitive तथा gerund में से किसी का भी प्रयोग किया जा सकता है।
advise, allow, attempt, begin, continue, hate, intend, learn, like, love, remember, start.

To-infinitive	Gerund
1. He intends to live here. 2. I love to hear this song. 3. I remembered to see him. 4. We prefer to travel by air. 5. He continued to write letters.	1. He intends living here. 2. Move hearing this song. 3. I remembered seeing him. 4. We prefer travelling by air. 5. He continued writing letters.

2. अनुभूति सम्बन्धी निम्नलिखित क्रियाओं के साथ bare-infinitive अथवा gerund में से किसी का भी प्रयोग किया जा सकता है :
feel, hear, notice, observe, see, watch.

Bare-Infinitive	Gerund
1. I heard her come in. 2. She saw me cross the road. 3. I heard you shout in the class.	1. I heard her coming in. 2. She saw me crossing the road. 3. I heard you shouting in the class.

3. निम्नलिखित क्रियाओं के साथ केवल gerund का ही प्रयोग किया जा सकता है। इनके साथ infinitive का प्रयोग कभी नहीं किया ‘
जाना चाहिए।
avoid, delay, deny, dislike, enjoy, finish, forget, imagine, keep (जारी रखना), mind (बुरा मनाना), pardon, postpone, risk, stop, suggest, try (परखना), understand.

4. निम्नलिखित क्रियाओं के साथ भी gerund का ही प्रयोग किया जाता है :

be worth, can’t bear, be no use, can’t stand, be no good, can’t help.

1. This table is worth buying.
2. It is no use crying over spilt milk.
3. It is no good imitating others.
4. She can’t bear living away from her children.
5. I can’t stand smoking in my room.
6. We couldn’t help laughing at him.

5. यदि किसी gerund से पूर्व कोई संज्ञा अथवा सर्वनाम लगा हो, तो यह अवश्य ही सम्बन्धवाचक रूप में होना चाहिए, जैसे

1. I dislike Mohan’s coming late daily.
2. Your father depends on your working hard.
3. Do you mind my smoking here?

Fill in the blanks with the correct form of the given verbs (Gerund or Infinitive) :

1. I don’t mind …………. (give) my book to you.
2. My father has stopped ………… (talk) to him.
3. We enjoyed …………… (swim) in the river.
4. She likes …………. (walk) in her garden.
5. He has given up …………. (smoke).
6. The tailor has completed ………….. (sew) the shirt.
7. He refused ………….. (accept) my advice.
8. When the bell rang, the students came
9. I decided ………. (see) the Principal.
10. She offered …………… (bring) flowers for me.
11. I want …………… (play) cricket.
12. Do you really enjoy …………. (play) football ?
13. My father can’t afford ………….. (buy) a T.V. set.
14. They will not permit you …………… (talk) in the library.
15. I advised my brother ………….. (work) hard for the test.

The participle

क्रिया के जिस रूप में Verb तथा Adjective दोनों के ही गुण हों, उसे Participle कहा जाता है। Participle तीन प्रकार के होते हैं :

Present Participle	Past Participle	Perfect Participle
Drowning	Drowned	Having drowned
Seeing	Seen	Having seen
Finishing	Finished	Having finished

1. Present Participle के कुछ उदाहरण

• A drowning man catches at a straw.
• The results were encouraging.
• Taking a walking stick, the old lady came out of the cottage.
• Seeing the police, the thief ran away.
• Naresh went into the bathroom singing.

2. Past Participle के कुछ उदाहरण

• His spoken English is much better than yours.
• These solved papers are very helpful.
• I boarded a crowded bus.
• I saw a faded rose.

3. Perfect Participle के कुछ उदाहरण

• Having bought a book, I came back from the market.
• Having done his homework, John went out to play.
• Having attended a meeting of the club, I came back.
• Having won a prize, Neelu felt happy.

4. Participle Phrases के कुछ उदाहरण
याद रखिए कि
(1) जब कोई क्रिया वाक्य की मुख्य क्रिया के समय पर ही हो रही हो तो उसके लिए Present Participle (V₁-ing) का प्रयोग किया जाना चाहिए :
I looked through some old papers and came across this letter.
= Looking through some old papers, I came across this letter.

The students saw the Headmaster and they stopped talking.
= Seeing the Headmaster, the students stopped talking.

(2) जब कोई क्रिया वाक्य की मुख्य क्रिया से पहले हो चुकी हो, तो उसके लिए Past Participle (having + V₃) का प्रयोग किया जाता है :
I met my friend and went back with him to his house.
= Having met my friend, I went back with him to his house.

The match ended and the spectators went away.
= The match having ended, the spectators went away.

Fill in the blanks with the correct non-finite form (Infinitive, Gerund or Participle) of the verbs given in the brackets :

1. The rice will grow well in the ………… (come) rains.
2. We heard of his ………… (come) back today.
3. We hope …………… (see) him back soon.
4. …………… (Believe) him to be right, I trusted him.
5. Night ………….. (come) on, the men went home.
6. Did you hear of his ………. (win) a prize ?
7. I am tired of …………. (do) this work.
8. Generally ……… (speak), we get what we deserve.
9. We saw him …………( leave) the house.
10. I was very happy ………… (see) you.
11. I shall be glad …….. (help) you.
12. My wife ……………… (expect) my return, did not leave the house.
13. ………….. (Spelt) is more difficult than …………. (write).
14. I am …………… (blame), not you.
15. The coach made us … (run).

Miscellaneous Sentences For Practice

Use the proper form of Non-finites in the following sentences

I.

1. ………………. (Teach) correct English needs great care.
2. People assembled ………………. (hear) the Minister.
3. I saw him ………………. (leave) his house.
4. Some people love ……………….(climb) mountains.
5 ……………….(Walk) is a good exercise.
6. It is easy ………………. (advise) others.
7. People worship the ………………. (rise) sun.
8. I made him ………………. (laugh).
9. A ………………. (drown) man catches at a straw.
10. I intend ……………….(spend) my vacation with my uncle.

II.

1. We are busy ………………. (pack).
2. He refused ………………. (obey) me orders.
3. I hope ………………. (succeed) in my plans.
4. The ………………. (steal) money did not last long.
5. He insisted on ………………. (see) him.
6. These days it is not easy ………………. (get) a job.
7. We were too ……………….(tire) to work.
8. I enjoy ………………. (piny) with small children.
9. ………………. (Smoke) is injurious to health.
10. She agreed ………………. (marry) the poor shepherd.

III.

1. They all heard him ………………. (sing).
2. The runner is ………………. (exhaust).
3. It is no use ………………. (wait) here now.
4. Are you interested in ………………. (paint) ?
5. Dogs are not allowed ………………. (enter) the garden.
6. ………………. (Swim) is a good exercise.
7. I heard him ………………. (cry) for help. .
8. Are you interested in ………………. (boat) ?
9. She was too tired ………………. (walk).
10. No ………………. (park) here.

IV.

1. I wonder why he avoids ………………. (meet) me.
2. It is no use ………………. (argue) with him.
3. I made him ………………. (feel!) sorry.
4. ………………. (Drink) ruins our health.
5. I don’t mind ………………. (wait).
6. He did not let me ………………. (play) in his garden.
7. I hope ………………. (get) first division in the examination.
8. I don’t want ………………. (swim) in the river.
9. I enjoy ………………. (sing) patriotic songs.

V.

1. His story made the listeners ………………. (weep).
2. Dancing is difficult ………………. (learn).
3. We enjoyed ………………. (boat) in the lake.
4. I saw the ball ………………. (roll) into the well.
5. We are looking forward to ………………. (see) her.
6. He used ………………. (smoke) in his youth.
7. How dare you ………………. (talk) like that ?
8. They found her ………………. (sleep).
9. They made her ………………. (sing) a song.
10. She refused ………………. (help).

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 8 Quadrilaterals Ex 8.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 8 Quadrilaterals Ex 8.1

Question 1.
The angles of a quadrilateral are in the ratio 3: 5 : 9: 13. Find all the angles of the quadrilateral.
Answer:
Let, ABCD be a given quadrilateral.
∴ ∠A : ∠B : ∠C : ∠D = 3 : 5 : 9 : 13
Sum of ratios = 3 + 5 + 9 + 13 = 30
In quadrilateral ABCD, ∠A + ∠B + ∠C + ∠D = 360°
∴ ∠A = \(\frac{3}{30}\) × 360° = 3 × 12 = 36°
∴ ∠B = \(\frac{5}{30}\) × 360° = 5 × 12 = 60°
∴ ∠C = \(\frac{9}{30}\) × 360° = 9 × 12 = 108°
∴ ∠D = \(\frac{13}{30}\) × 360° = 13 × 12 = 156°
Thus the angles of the given quadrilateral are 36°, 60°, 108° and 156°.

Question 2.
If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Answer:
In parallelogram ABCD, diagonals are equal.
∴ AC = BD.
In ∆ DAB and ∆ CBA.
DA = CB (Theorem 8.2)
AB = BA (Common)
DB = CA (Given)
∴ ∆ DAB ≅ ∆ CBA sss rule)
∴ ∠ DAB = ∠CBA (CPCT)
In parallelogram ABCD, AD || BC and AB is their transversal.
∴ ∠ DAB + ∠ CBA = 180°
(Interior angles on the same side of transversal)
Thus, in parallelogram ABCD, two angles ∠A and∠B are right angles. Hence, all the angles are right angle.
Hence, the parallelogram ABCD having equal diagonals is a rectangle.

Question 3.
Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Answer:
In quadrilater ABCD. diagonals AC and BD bisect each other at M at right angles.
∴ AM = CM, BM = DM and
∠AMB = ∠CMB = ∠CMD = ∠AMD = 90°.
In ∆ AMB and ∆ CMB,
AM = CM
∠ AMB = ∠CMB
BM = BM (Common)
∴ ∆ AMB ≅ ∆ CMB (SAS rule)
∴ AB = CB (CPCT)
Similarly, proving ∆ BMC ≅ ∆ DMC and ∆ DMA ≅ ∆ BMA, we get BC = DC and DA = BA.
Thus, in quadrilateral. ABCD.
AB = BC CD = DA.
Therefore, quadrilateral ABCD is a rhombus.
Thus, if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Question 4.
Show that the diagonals of a square are equal and bisect each other at right angles.

Answer:
ABCD is a square in which diagonals AC and BD intersect at M.
Every square is a parallelogram.
∴ AC and BD bisect each other. …………… (1)
In ∆ DAB and ∆ CBA,
DA = CB (Sides of a square)
∠ DAB = ∠ CBA (Right angles in a square)
AB = BA (Common)
∴ ∆ DAB ≅ ∆ CBA (SAS rule)
∴ BD = AC (CPCT) ……………….. (2)
Now, in ∆ AMB and ∆ CMB,
AM = CM (BD bisects AC at M).
BM = BM (Common)
AB = CB (Sides of a square)
∴ ∆ AMB ≅ ∆ CMB (SSS rule)
∴ ∠ AMB = ∠CMB (CPCT)
But, ∠ AMB and ∠ CMB form a linear pair.
∴ ∠ AMB + ∠ CMB = 180°
Hence, ∠AMB = ∠ CMB = 90° (3)
(1), (2) and (3) taken together proves that the diagonals of a square are equal and bisect each other at right angles.

Question 5.
Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Answer:
In quadrilateral ABCD, diagonals AC and BD are equal and bisect each other at right angles.
∴ AC = BD,
MA = MC = MB = MD = \(\frac{1}{2}\)AC = \(\frac{1}{2}\)BD and
∠AMB = ∠CMB= ∠DMC = ∠DMA= 90°.
In ∆ AMB and ∆ CMB,
AM = CM
∠ AMB = ∠ CMB (Right angles)
BM = BM (Common)
∴ ∆ AMB ≅ ∆ CMB (SAS rule)
∴ AB = CB (CPCT)
Similarly, we can prove that BC = DC and
DA = BA.
Thus, in quadrilateral ABCD,
AB = BC = CD = DA …………… (1)
Now, in ∆ DAB and ∆ CBA,
DA = C B
BD = AC (Given)
AB = BA (Common)
∴ ∆ DAB ≅ ∆ CBA (SSS rule)
∴ ∠DAB = ∠CBA (CPCT)
Thus, in quadrilateral ABCD, ∠A = ∠B.
Similarly, we can prove that ∠B = ∠C and ∠C = ∠D.
Thus, in quadrilateral ABCD,
∠A = ∠B = ∠C = ∠D.
Moreover. In quadrilateral ABCD,
∠A + ∠B + ∠C + ∠D = 360°
∴ ∠A = ∠B = ∠C = ∠D = \(\frac{360^{\circ}}{4}\) = 90° ……………… (2)
Thus, (1) and (2) taken together proves that in quadrilateral ABCD, all the sides are equal and all the angles are equal.
Therefore, quadrilateral ABCD is a square.
Thus, if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Question 6.
Diagonal AC of a parallelogram ABCD bisects ∠A (see the given figure). Show that (i) it bisects ∠C also, (ii) ABCD is a rhombus.

Answer:
Diagonal AC of parallelogram ABCD bisects ∠A.
∴ ∠DAC = ∠BAC …………… (1)
Now, ∠BAC and ∠DCA are alternate angles formed by transversal AC of AB || CD.
∴ ∠BAC = ∠DCA …………… (2)
Similarly, ∠DAC and ∠BCA are alternate angles formed by transversal AC of AD || BC.
∴ ∠DAC = ∠BCA ……………… (3)
From (1), (2) and (3),
∠DCA = ∠BCA.
But, ∠DCA + ∠BCA = ∠BCD (Adjacent angles)
∴ AC bisects ∠C also.
In parallelogram ABCD,
∠A = ∠C (Theorem 8.4)
∴ \(\frac{1}{2}\)∠A = \(\frac{1}{2}\)∠C
∴ ∠ DAC = ∠ DCA
∴ In ∆ DAC, DA = DC (Sides opposite to equal angles)
Moreover, in parallelogram ABCD,
AB = CD and BC = DA (Theorem 8.2)
∴ AB = BC = CD = DA
Thus. In parallelogram ABCD, all the sides are equal.
Hence, ABCD is a rhombus.

Question 7.
ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.
Answer:

ABCD is a rhombus
∴ AB || DC, BC || AD and AB = BC = CD = DA.
AB || DC and AC is their transversal.
∴ ∠CAB = ∠ACD (Alternate angles)
In, ∆ DAC, CD = DA
∴ ∠ACD = ∠CAD
Then, ∠CAB = ∠CAD
But, ∠CAB + ∠CAD = ∠ DAB (Adjacent angles)
∴ ∠ CAB = ∠CAD = \(\frac{1}{2}\) ∠DAB
This shows that AC bisects ∠A.
Again, BC || AD and AC is their transversal.
∴ ∠ BCA = ∠ DAC (Alternate angles)
In, ∆ DAC, DA = DC
∴ ∠ DAC = ∠ DCA
Then, ∠BCA = ∠DCA
But, ∠ BCA + ∠ DCA = ∠ DCB (Adjacent angles)
∴ ∠ BCA = ∠ DCA = \(\frac{1}{2}\)∠ DCB
This shows that AC bisects ∠C.
Thus, AC bisects ∠A as well as ∠C.
Similarly, taking BD as transversal of AB || DC, and BC || AD, it can be proved that BD bisects ∠B as well as ∠D.

Question 8.
ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that: (i) ABCD is a square. (ii) Diagonal BD bisects ∠B as well as ∠D.
Answer:

In rectangle ABCD, AB = CD, BC = AD, AB || CD and BC || AD.
AC bisects ∠A as well as ∠C.
∴ ∠DAC = ∠BAC = \(\frac{1}{2}\)∠A and
∠ DCA = ∠ BCA = \(\frac{1}{2}\)∠C
Now, AB || CD and AC is their transversal.
∴ ∠ BAC = ∠ DCA (Alternate angles)
∴ ∠ DAC = ∠ DCA
Thus, in ∆ DAC, ∠DAC = ∠DCA
∴ AD = CD (Sides opposite to equal angles)
From this, we get AB = BC = CD = DA.
Also, in rectangle ABCD,
∠A = ∠B = ∠C = ∠D = 90°
Hence, ABCD is a square. …..Result (i)
In ∆ BCD, BC = CD
∴ ∠ CBD = ∠ CDB
Moreover, AB || CD and BD is their transversal.
∴ ∠ CDB = ∠ ABD (Alternate angles)
∴ ∠ CBD = ∠ ABD
Now, ∠ CBD + ∠ ABD = ∠ ABC
∴ ∠ CBD = ∠ ABD = \(\frac{1}{2}\) ∠ ABC
Thus, BD bisects ∠B.
Similarly, diagonal BD bisects ∠ D.
Hence, diagonal BD bisects ∠B as well as ∠D …….. Result (ii)

Question 9.
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see the given figure). Show that:
(i) ∆ APD ≅ ∆ CQB
(ii) AP = CQ
(iii) ∆ AQB ≅ ∆ CPD
(iv) AQ = CP
(v) APCQ is a parallelogram.
Answer:

ABCD is a parallelogram.
∴ AD || BC and BD is their transversal.
∴ ∠ADB = ∠CBD (Alternate angles)
∴ ∠ADP = ∠CBQ …………… (1)
Similarly, CD || BA and BD is their transversal.
∴ ∠ ABD = ∠ CDB (Alternate angles)
∴ ∠ABQ = ∠CDP ……………… (2)
In ∆ APD and ∆ CQB,
AD = CB (Opposite sides of a parallelogram)
∠ ADP = ∠ CBQ [by (1)]
DP = BQ (Given)
∴ ∆ APD ≅ ∆ CQB (SAS rule) ……. Result (i)
∴ AP = CQ (CPCT) …… Result (ii)
In ∆ AQB and ∆ CPD,
AB = CD (Opposite sides of a parallelogram)
∠ ABQ = ∠ CDP [by (2)]
BQ = DP (Given)
∴ ∆ AQB ≅ ∆ CPD (SAS rule) …….. Result (iii)
∴ AQ = CP (CPCT) ………….. Result (iv)
Now, in quadrilateral APCQ, AP = CQ and AQ = CP
Hence, by theorem 8.3, APCQ is a parallelogram. ………. Result (v)

Question 10.
ABCD is a parallelogram and AP and Cg are perpendiculars from vertices A and C on diagonal BD (see the given figure). Show that
(i) ∆ APB ≅ ∆ CQD
(ii) AP = CQ

Answer:
In parallelogram ABCD, AB || CD and BD is their transversal.
∴ ∠ ABD = ∠ CDB (Alternate angles)
∴ ∠ABP = ∠CDQ ……………. (1)
Now, in ∆ APB and ∆ CQD,
AB = CD (Opposite sides of a parallelogram)
∠ ABP = ∠ CDQ [by (1)]
∠ APB = ∠ CQD (Right angles)
∆ APB ≅ ∆ CQD (AAS rule) ………… Result (i)
∴ AP = CQ (CPCT) ……….. Result (ii)

Question 11.
In ∆ ABC and ∆ DBF, AB = DE, AB || DE, j BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see the given figure). Show that:
(i) Quadrilateral ABED is a parallelogram
(ii) Quadrilateral BEFC is a parallelogram
(iii) AD || CF and AD = CF
(iv) Quadrilateral ACFD is a parallelogram
(v ) AC = DF
(vi) ∆ ABC ≅ ∆ DEF.

Answer:
In quadrilateral ∆ BED, AB = DE and AB || DE. Thus, in quadrilateral ABED, sides in one s pair of opposite sides are equal and parallel. Hence, by theorem 8.8, quadrilateral ABED is a parallelogram. …… Result (i)
Similarly, in quadrilateral BEFC, BC = EF and BC || EF.
Hence, by theorem 8.8, quadrilateral BEFC is a parallelogram. …………. Result (ii)
In parallelogram ABED, AD || BE and in parallelogram BEFC, BE || CE Thus, AD and CF both are parallel to BE.
∴ AD || CF ……….(1)
In parallelogram ABED, AD = BE and in parallelogram BEFC, BE = CF.
∴ AD = CF ……… (2)
Taking (1) and (2) together, we get
AD || CF and AD = CF ………. Result (iii)
In quadrilateral ACFD, AD || CF and AD = CF. Hence, by theorem 8.8, quadrilateral ACFD is a parallelogram. ………. Result (iv)
AC and DF are opposite sides of parallelogram ACFD.
∴ AC = DF ………….. Result (v)
Now, in ∆ ABC and ∆ DEF,
AB = DE (Given)
BC = EF (Given)
AC = DF [by result (v)l
∴ ∆ ABC ≅ ∆ DEF (SSS rule) …… Result (vi)

Question 12.
ABCD is a trapezium in which AB || CD and AD = BC (see the given figure). Show that:
(i) ∠A = ∠B
(ii) ∠C = ∠D
(iii) ∆ ABC ≅ ∆ BAD
(iv) diagonal AC = diagonal BD
[Hint: Extend AB and draw a line through C parallel to DA intersecting AB produced at E.)

Answer:
AB is extended to E, and AB || CD.
∴ AE || CD
In quadrilateral ADCE, AE || CD and by consturction CE || DA.
∴ Quadrilateral ADCE is a parallelogram.
∴ AD = CE
Moreover, AD = BC (Given)
∴ BC = CE
In ∆ BCE, BC = CE
∴ ∠CBE = ∠CEB
∴ ∠CBE = ∠CEA ………….. (1)
In parallelogram ADCE, AD || CE and AE is their transversal.
∴ ∠ DAE + ∠ CEA = 180° (Interior angles on the same side of transversal)
∴ ∠ DAE + ∠ CBE = 180° [by (1)]
∴ ∠ DAE = 180° – ∠ CBE …………… (2)
Moreover, ∠ ABC + ∠ CBE = 180° (Linear pair)
∴ ∠ ABC = 180° – ∠ CBE …………. (3)
From (2) and (3),
∠ DAE = ∠ ABC
∴ ∠A = ∠B ……… Result (i)
AB || CD and AD is their transversal.
∴ ∠A + ∠D = 180°
∴ ∠D = 180°- ∠A ………….. (4)
AB || CD and BC is their transversal.
∴ ∠B + ∠C = 180°
∴ ∠C = 180°- ∠B
∴ ∠C = 180° – ∠ A [by result (i)] ……… (5)
From (4) and (5),
∠C = ∠D …….. Result (ii)
Draw diagonals AC and BD.
In ∆ ABC and ∆ BAD,
BC = AD (Given)
∠ ABC = ∠ BAD [by result (i)]
AB = BA (Common)
∴ ∆ ABC ≅ ∆ BAD (SAS rule) ………. Result (iii)
∴ AC = BD (CPCT)
Thus, diagonal AC = diagonal BD … Result (iv)
Note: A trapezium in which non-parallel sides are equal is called an isosceles trapezium. As proved above, in an isosceles trapezium, the diagonals are equal and the angles on each parallel side are equal.

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 7 Triangles Ex 7.5 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5

Question 1.
ABC is a triangle. Locate a point in the interior of ∆ ABC which is equidistant from all the vertices of ∆ ABC.
Answer:

In ∆ ABC, draw l, the perpendicular bisector of side AB and m, the perpendicular bisector of side BC. Name the point of intersection of l and m as P.
P is a point on the perpendicular bisector of AB. Hence, P is equidistant from A and B.
∴ PA = PB
P is a point on the perpendicular bisector of BC. Hence, P is equidistant from B and C.
∴ PB = PC
Thus, PA = PB = PC
Hence, P is the required point which is equidistant from all the vertices of ∆ ABC.
Note: Since ∆ ABC given here is an acute angled triangle, point P lies in the interior of ∆ ABC. If ∆ ABC is a right angled Mangle, point P lies on the hypotenuse. Actually, in that case, point P will be the midpoint of the hypotenuse. Lastly, if ∆ ABC is an obtuse angled triangle, point P lies in the exterior of ∆ ABC. This point P is called the circumcentre of ∆ ABC.

Question 2.
In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.

Answer:
In ∆ ABC, draw the bisectors of ∠B and ∠C to intersect each other at point I.
I is a point on the bisector of ∠ B. Hence, I is equidistant from sides BA and BC. Similarly, I is a point on the bisector of ZC. Hence, I is equidistant from sides BC and CA.
Thus, point I is the required point which is equidistant from all the three sides AB, BC and CA of ∆ ABC.
This point I is called the incentre of ∆ ABC. It always lies in the interior of ∆ ABC irrespective of the type of ∆ ABC.

Question 3.
In a huge park, people are concentrated at three points (see the given figure):

A: where there are different slides and swings for children.
B: near which a man-made lake is situated.
C: which is near to a large parking and exit.
Where should an ice cream parlour be set up so that maximum number of persons can approach it ?
(Hint: The parlour should be equidistant from A, B and C.)
Answer:
First of all, construct ∆ ABC with the given points A, B and C as vertices. Then, as shown in example 1, draw the perpendicular s bisectors of any two sides of ∆ ABC and name their point of intersection as P.

Now, the ice cream parlour should be set up at the location given by point P as it is equidistant from all the three places (points) A, B and C.

Question 4.
Complete the hexagonal and star shaped < Rangolies [see figure (1) and (2)] by filling them with as many equilateral triangles of > side 1 cm as you can. Count the number < of triangles in each case. Which has more triangles?

Answer:
In figure (1), if we join the opposite vertices, we get three longest diagonals of hexagon ABCDEE By the intersection of these diagonals we get point O and six equilateral triangles – ∆ OAB, ∆ OBC, ∆ OCD, ∆ ODE, ∆ OEF and ∆ OFA. Each side of all these equilateral triangles will measure 5 cm. In each of these six triangles, we can fill 25 (1 + 3 + 5 + 7 + 9) equilateral triangles with side 1 cm each. Hence in the hexagonal Rangoli ABCDEF, we can fill 25 × 6 = 150 triangles.

Similarly, in figure (2), we can fill 150 triangles in the inner hexagon and 150 triangles in the six triangles on the boundary of the hexagon. Thus, in figure (2), 150 + 150 = 300 triangles can be filled.
Hence, more triangles can be filled in figure (2).

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 7 Triangles Ex 7.4 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.4

Question 1.
Show that in a right angled triangle, the hypotenuse is the longest side.
Answer:

In ∆ ABC, ∠ B is a right angle.
∴ ∠ B = 90° and AC is the hypotenuse.
In ∆ ABC,
∠A + ∠B + ∠C = 180°
∴ ∠ A + 90° + ∠ C = 180°
∴ ∠ A + ∠ C = 90°
Now, ∠ A and ∠ C are both positive (in degrees) and their sum is 90°.
∴ ∠ A < 90° and ∠ C < 90°
∴ ∠ A < Z B and ∠ C < ∠ B
∴ BC < AC and AB < AC (Theorem 7.7)
Hence, hypotenuse AC is greater than each of the other two sides BC and AB. Thus, the hypotenuse is the longest side in a right angled triangle.

Question 2.
In the given figure, sides AB and AC of ∆ ABC are extended to points P and Q respectively. Also, ∠PBC < ∠ QCB. Show that AC > AB.

Answer:
∠ PBC < ∠ QCB (Given)
∴ – ∠ PBC > – ∠ QCB (Multiplying an inequality by (-1), it reverses)
∴ 180° – ∠ PBC > 180° – ∠ QCB (Adding 180° on both the sides) …………. (1)
Now, ∠ ABC and ∠ PBC as well as ∠ ACB and ∠ QCB from a linear pair.
∴ ∠ ABC = 180° – ∠ PBC and
∠ ACB = 180° – ∠ QCB
Substituting these values in (1), we get
∠ ABC > ∠ ACB
Now, in ∆ ABC, ∠ ABC > ∠ ACB A
∴ AC > AB (Theorem 7.7)

Question 3.
In the given figure, ∠ B < ∠ A and ∠ C < ∠ D. Show that AD < BC.

Answer:
In ∆ OAB, ∠ B < ∠ A
∴ OA < OB (Theorem 7.7) …………….. (1)
In ∆ OCD, ∠ C < ∠ D
∴ OD < OC (Theorem 7.7) ……………… (2)
Adding (1) and (2),
OA + OD < OB + OC
∴ AD < BC (As O is the point of intersection of AD and BC, it lies on both the line segments.)

Question 4.
AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD ,(see the given figure). Show that ∠A > ∠C and ∠B > ∠D.

Answer:

Construction: In quadrilateral ABCD, draw diagonal AC.
AB is the smallest side of ABCD and CD is the longest side of ABCD.
∴ AB < BC and AD < CD.
In ∆ ABC, AB < BC
∴ ∠ ACB < ∠ BAC …… (1)
In ∆ CDA, AD < CD
∴ ∠ DCA < ∠ DAC ……… (2)
Adding (1) and (2),
∠ ACB + ∠ DCA < ∠ BAC + ∠ DAC
∴ ∠ BCD < ∠ BAD
∴ ∠ BAD > ∠ BCD
Thus, in quadrilateral ABCD, ∠ A > ∠ C. Similarly, after constructing diagonal BD and using the inequalities in A ABD and A CBD, it can be proved that ∠ B > ∠ D.

Question 5.
In the given figure, PR > PQ and PS bisects ∠ QPR. Prove that ∠ PSR > ∠ PSQ.

Answer:
PS is the bisector of ∠QPR.
∴ ∠QPS = ∠RPS = \(\frac{1}{2}\) ∠QPR ……………. (1)
∠ PSR is an exterior angle of A PQS and ∠ PSQ is an exterior angle of A PRS.
∴ PSR = ∠ Q + ∠QPS and
∠PSQ = ∠R + ∠RPS …………….. (2)
Now, in A PQR, PR > PQ
∴ ∠ Q > ∠ R
∴ ∠Q + \(\frac{1}{2}\) ∠ QPR > ∠R + \(\frac{1}{2}\) ∠ QPR
∴ ∠Q + ∠QPS > ∠R + ∠RPS [from (1)]
∴ ∠PSR > ∠PSQ

Question 6.
Show that of all line segments drawn from a given point not on a given line, the perpendicular line segment is the shortest.
Answer:

AB is a line and P is a point not on AB.
PM is the perpendicular line segment drawn from P to line AB.
N is any point on AB, other than M.
In ∆ PMN, ∠ M = 90°
∴ ∠ N < 90°
Thus, in ∆ PMN, ZN < ZM.
∴ PM < PN
This is true for any location of point N.
Hence, of all the line segments drawn from a point not on a given line, the, perpendicular line segment is the shortest.

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 7 Triangles MCQ Questions with Answers.

PSEB 9th Class Maths Chapter 7 Triangles MCQ Questions

Multiple Choice Questions and Answer

Answer each question by selecting the proper alternative from those given below each question to make the statement true:

Question 1.
In ∆ ABC, ∠A = ∠C, AC = 5 and BC = 4. Then, the perimeter of ∆ ABC is ……………. .
A. 9
B. 14
C. 13
D. 15
Answer:
C. 13

Question 2.
In ∆ PQR, PQ = PR, QR is extended to S and ∠PRS = 110°. Then, ∠PQR = ……………… .
A. 30°
B. 50°
C. 80°
D. 70°
Answer:
D. 70°

Question 3.
In ∆ ABC and ∆ DEF, AB = DE, BC = EF and ∠B = ∠E. If the perimeter of ∆ ABC is 20, then the perimeter of ∆ DEF is ……………. .
A. 10
B. 20
C. 15
D. 40
Answer:
B. 20

Question 4.
In ∆ ABC and ∆ PQR, AB = PQ, ∠A = ∠P and ∠B = ∠Q. If ∠A + ∠C = 130°, then ∠Q = …………….. .
A. 65°
B. 130°
C. 50°
D. 100°
Answer:
C. 50°

Question 5.
In ∆ PQR, ∠P = ∠Q = ∠R. If PQ = 6, then the perimeter of ∆ PQR is ………………. .
A. 12
B. 9
C. 18
D. 24
Answer:
C. 18

Question 6.
In ∆ ABC, AB < AC. Then …………… holds good.
A. ∠A < ∠B
B. ∠B < ∠C
C. ∠C < ∠A
D. ∠C < ∠B
Answer:
D. ∠C < ∠B

Question 7.
In ∆ PQR, ∠R > ∠Q. Then, ………………. holds good.
A. PQ > PR
B. QR > PQ
C. PR > PQ
D. PQ > QR
Answer:
A. PQ > PR

Question 8.
In ∆ ABC, AB > BC and BC > AC. Then, the smallest angle of ∆ ABC is …………………. .
A. ∠A
B. ∠C
C. ∠B
D. ∠A or ∠C
Answer:
C. ∠B

Question 9
………………….. cannot be the measures of the sides of a triangle.
A. 10, 12, 14
B. 2, 3, 4
C. 8, 9, 10
D. 2, 4, 10
Answer:
D. 2, 4, 10

Question 10.
In ∆ PQR, PQ = 4, QR = 6 and PR = 5. Then, …………….. is the angle with greatest measure in ∆ PQR.
A. ∠P
B. ∠Q
C. ∠R
D. ∠QRP
Answer:
A. ∠P

Question 11.
In ∆ XYZ, ∠X = 45° and ∠Z = 60°. Then, …………….. is the longest side of ∆ XYZ.
A. XY
B. YZ
C. XZ
D. XY or YZ
Answer:
C. XZ

Question 12.
In ∆ ABC, ∠B = 30° and BC is extended to D. If ∠ACD = 110°, then the longest side of ∆ ABC is ………………. .
A. AB
B. BC
C. CA
D. AB or AC
Answer:
B. BC

Question 13.
In ∆ ABC, AB = 4 and BC = 7, Then, ……………… holds good.
A. AC < 7
B. AC > 4
C. 4 < AC < 7
D. 3 < AC < 11
Answer:
D. 3 < AC < 11

Question 14.
In ∆ PQR, PQ = 3 and QR = 7. Then, …………….. holds good.
A. PR = 4
B. PR = 10
C. 10 > PR > 4
D. 7 > PR > 3
Answer:
C. 10 > PR > 4

Question 15.
In ∆ ABC, the bisectors of ∠B and ∠C intersect at I. If ∠A = 70°, then ∠BIC = ………………… .
A. 35°
B. 75°
C. 100°
D. 125°
Answer:
D. 125°