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GRAMMAR CBSE NOTES CLS 6 7 8 9 10 11 12 MCQ QUESTIONS NCERT BOOKS STUDY MATERIAL NUMBERS CALCULATOR Learn CBSE NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12 NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals Ex 8.1 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals Ex 8.1. NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals Ex 8.1 Ex 8.1 Class 9 Maths Question 1. The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral. Solution: Let the angles of the quadrilateral be 3x, 5x, 9x and 13x. ∴ 3x + 5x + 9x + 13x = 360° [Angle sum property of a quadrilateral] ⇒ 30x = 360° ⇒ x = 360∘30 = 12° ∴ 3x = 3 x 12° = 36° 5x = 5 x 12° = 60° 9x = 9 x 12° = 108° 13a = 13 x 12° = 156° ⇒ The required angles of the quadrilateral are 36°, 60°, 108° and 156°. Ex 8.1 Class 9 Maths Question 2. If the diagonals of a parallelogram are equal, then show that it is a rectangle. Solution: Let ABCD is a parallelogram such that AC = BD. In ∆ABC and ∆DCB, AC = DB [Given] AB = DC [Opposite sides of a parallelogram] BC = CB [Common] ∴ ∆ABC ≅ ∆DCB [By SSS congruency] ⇒ ∠ABC = ∠DCB [By C.P.C.T.] …(1) Now, AB || DC and BC is a transversal. [ ∵ ABCD is a parallelogram] ∴ ∠ABC + ∠DCB = 180° … (2) [Co-interior angles] From (1) and (2), we have ∠ABC = ∠DCB = 90° i.e., ABCD is a parallelogram having an angle equal to 90°. ∴ ABCD is a rectangle. Ex 8.1 Class 9 Maths Question 3. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. Solution: Let ABCD be a quadrilateral such that the diagonals AC and BD bisect each other at right angles at O. ∴ In ∆AOB and ∆AOD, we have AO = AO [Common] OB = OD [O is the mid-point of BD] ∠AOB = ∠AOD [Each 90] ∴ ∆AQB ≅ ∆AOD [By,SAS congruency ∴ AB = AD [By C.P.C.T.] ……..(1) Similarly, AB = BC .. .(2) BC = CD …..(3) CD = DA ……(4) ∴ From (1), (2), (3) and (4), we have AB = BC = CD = DA Thus, the quadrilateral ABCD is a rhombus. Alternatively : ABCD can be proved first a parallelogram then proving one pair of adjacent sides equal will result in rhombus. Ex 8.1 Class 9 Maths Question 4. Show that the diagonals of a square are equal and bisect each other at right angles. Solution: Let ABCD be a square such that its diagonals AC and BD intersect at O. (i) To prove that the diagonals are equal, we need to prove AC = BD. In ∆ABC and ∆BAD, we have AB = BA [Common] BC = AD [Sides of a square ABCD] ∠ABC = ∠BAD [Each angle is 90°] ∴ ∆ABC ≅ ∆BAD [By SAS congruency] AC = BD [By C.P.C.T.] …(1) (ii) AD || BC and AC is a transversal. [∵ A square is a parallelogram] ∴ ∠1 = ∠3 [Alternate interior angles are equal] Similarly, ∠2 = ∠4 Now, in ∆OAD and ∆OCB, we have AD = CB [Sides of a square ABCD] ∠1 = ∠3 [Proved] ∠2 = ∠4 [Proved] ∴ ∆OAD ≅ ∆OCB [By ASA congruency] ⇒ OA = OC and OD = OB [By C.P.C.T.] i.e., the diagonals AC and BD bisect each other at O. …….(2) (iii) In ∆OBA and ∆ODA, we have OB = OD [Proved] BA = DA [Sides of a square ABCD] OA = OA [Common] ∴ ∆OBA ≅ ∆ODA [By SSS congruency] ⇒ ∠AOB = ∠AOD [By C.P.C.T.] …(3) ∵ ∠AOB and ∠AOD form a linear pair. ∴∠AOB + ∠AOD = 180° ∴∠AOB = ∠AOD = 90° [By(3)] ⇒ AC ⊥ BD …(4) From (1), (2) and (4), we get AC and BD are equal and bisect each other at right angles. Ex 8.1 Class 9 Maths Question 5. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. Solution: Let ABCD be a quadrilateral such that diagonals AC and BD are equal and bisect each other at right angles. Now, in ∆AOD and ∆AOB, We have ∠AOD = ∠AOB [Each 90°] AO = AO [Common] OD = OB [ ∵ O is the midpoint of BD] ∴ ∆AOD ≅ ∆AOB [By SAS congruency] ⇒ AD = AB [By C.P.C.T.] …(1) Similarly, we have AB = BC … (2) BC = CD …(3) CD = DA …(4) From (1), (2), (3) and (4), we have AB = BC = CD = DA ∴ Quadrilateral ABCD have all sides equal. In ∆AOD and ∆COB, we have AO = CO [Given] OD = OB [Given] ∠AOD = ∠COB [Vertically opposite angles] So, ∆AOD ≅ ∆COB [By SAS congruency] ∴∠1 = ∠2 [By C.P.C.T.] But, they form a pair of alternate interior angles. ∴ AD || BC Similarly, AB || DC ∴ ABCD is a parallelogram. ∴ Parallelogram having all its sides equal is a rhombus. ∴ ABCD is a rhombus. Now, in ∆ABC and ∆BAD, we have AC = BD [Given] BC = AD [Proved] AB = BA [Common] ∴ ∆ABC ≅ ∆BAD [By SSS congruency] ∴ ∠ABC = ∠BAD [By C.P.C.T.] ……(5) Since, AD || BC and AB is a transversal. ∴∠ABC + ∠BAD = 180° .. .(6) [ Co – interior angles] ⇒ ∠ABC = ∠BAD = 90° [By(5) & (6)] So, rhombus ABCD is having one angle equal to 90°. Thus, ABCD is a square. Ex 8.1 Class 9 Maths Question 6. Diagonal AC of a parallelogram ABCD bisects ∠A (see figure). Show that (i) it bisects ∠C also, (ii) ABCD is a rhombus. Solution: We have a parallelogram ABCD in which diagonal AC bisects ∠A ⇒ ∠DAC = ∠BAC (i) Since, ABCD is a parallelogram. ∴ AB || DC and AC is a transversal. ∴ ∠1 = ∠3 …(1) [ ∵ Alternate interior angles are equal] Also, BC || AD and AC is a transversal. ∴ ∠2 = ∠4 …(2) [ v Alternate interior angles are equal] Also, ∠1 = ∠2 …(3) [ ∵ AC bisects ∠A] From (1), (2) and (3), we have ∠3 = ∠4 ⇒ AC bisects ∠C. (ii) In ∆ABC, we have ∠1 = ∠4 [From (2) and (3)] ⇒ BC = AB …(4) [ ∵ Sides opposite to equal angles of a ∆ are equal] Similarly, AD = DC ……..(5) But, ABCD is a parallelogram. [Given] ∴ AB = DC …(6) From (4), (5) and (6), we have AB = BC = CD = DA Thus, ABCD is a rhombus.

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Can anyone translate this sentence? Fast alle deutschen städt haben eine fußgängerzone.

Posted by Christina Shaju 5 years, 1 month ago (10021301)

CBSE > Class 08 > German

5 answers

Kandula Mohan . Sai Pranav 5 years ago (9922702)

?? keep correct answer ??

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Kandula Mohan . Sai Pranav 5 years ago (9922702)

He asked you anser no more unusual answered

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Kandula Mohan . Sai Pranav 5 years ago (9922702)

You think he don't no

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Kandula Mohan . Sai Pranav 4 years, 10 months ago (9922702)

Shutup

4 Thank You

Vaibhav Mathur 4 years, 10 months ago (6817576)

Seacrh this line on google translate

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ANSWER

Give two examples of work

Posted by Shivam Pal 5 years, 1 month ago (8680564)

CBSE > Class 12 > Home Science

2 answers

Pooja Yadav 5 years ago (10118355)

Walking up stairs,shooting a bullet

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Sinamso Chipui 5 years ago (9278984)

Like working in the factory

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</a>

Posted by Aadya Singh 5 years, 1 month ago (10036784)

CBSE > Class 11 > Physics

3 answers

Aseem Mahajan 5 years, 1 month ago (7640926)

1 Thank You

Aseem Mahajan 5 years, 1 month ago (7640926)

Upper one is moving with greater velocity. He will land forward than below

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Aadya Singh 5 years, 1 month ago (10036784)

Give reason also ?

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ताकत को परिभाषित करें और उनके प्रकार पर चर्चा करें

Posted by Aarti Gupta 5 years, 1 month ago (10073057)

CBSE > Class 11 > शारीरिक शिक्षा

0 answers

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LMN Ltd. is feeling its income tax returns on time they are also updating their share holders about their projects and provide for return to them towards which interest group are they fulfilling there is possibility which values are being followed by the Co.

Posted by Tanishq Sharma 5 years ago (10091299)

CBSE > Class 11 > Business Studies

0 answers

ANSWER

Which think make Asteroids

Posted by Shruti Yadav 5 years, 1 month ago (1938188)

CBSE > Class 06 > Social (OLD)

2 answers

Angel Jindal 5 years ago (9544667)

Asteroids are small rocks moving in space between Mars and Jupiter

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Shweta Raj 5 years ago (10094232)

Asteroid are small rocks moving in space between mars and Jupiter

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Parveen draws an qudrat a bill of exchange for three months after sight for 1500 on 1st january, 2018

Posted by Love Singh 5 years, 1 month ago (10091259)

CBSE > Class 11 > Accountancy

0 answers

ANSWER

Yrr conversion kaise sikhe mujhe bilkul nahi aa raha please help in me in that

Posted by Diksha Singh 5 years, 1 month ago (10035434)

CBSE > Class 12 > Chemistry

4 answers

Gourav Sharma 5 years ago (10000673)

Aur btao kya puchna h

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Diksha Singh 5 years ago (10035434)

Waise questions board ke ncert exercise me se hi aaenge kya

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Gurneet Singh 5 years ago (10040721)

Same here

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Aditya Singh 5 years, 1 month ago (3673579)

Diksha if you want to learn conversions so learn all the named reactions in all chapters

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Sugest some way to save oil

Posted by Hlo Bro 5 years, 1 month ago (10091210)

CBSE > Class 05 > EVS

0 answers

ANSWER

Tell

Posted by Hlo Bro 5 years, 1 month ago (10091210)

CBSE > Class 05 > EVS

1 answers

Sashmitha Dhanasekar 5 years ago (10076341)

What

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Find the magnitude and direction of the resultant of two vectors A and B in terms of their magnitude and angle theta between them. By triangle law of vector addition

Posted by Tanisha Nehra 5 years, 1 month ago (10091198)

CBSE > Class 11 > Physics

2 answers

Aseem Mahajan 5 years, 1 month ago (7640926)

$$\vec{R}$$ *

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Aseem Mahajan 5 years, 1 month ago (7640926)

$$|\vect{R}| = \sqrt{A^2 + B^2 + 2ABcos\theta}$$
$$tan \theta = \dfrac{B cos \theta}{A + B sin \theta}$$

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What is square cube of 9999

Posted by Kunal Ranjan 5 years, 1 month ago (9671716)

CBSE > Class 08 > Mathematics

1 answers

Diksha Laniya🐥 5 years ago (10085318)

The ans is: 21. 5436

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A cycle of ₹700

Posted by Muhammed Arafath 5 years, 1 month ago (10012900)

CBSE > Class 08 > Mathematics

1 answers

Zibiah Gonsalves 5 years, 1 month ago (3780094)

Very good cost for a cycle

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Wind:_________ : water : coconut

Posted by Abhay Abhay Singh 5 years ago (9422617)

CBSE > Class 05 > Science

3 answers

Sde Ecity 3 years, 2 months ago (13520162)

drumstic (seed dispersal methods)

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Ridhima Sharma 4 years, 10 months ago (10507343)

Cotton

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? " 5 years ago (10153734)

Air

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Define function?

Posted by Ritika Morya 5 years, 1 month ago (9905039)

CBSE > Class 11 > Mathematics

2 answers

Deepanshu Jha 5 years ago (9962215)

Function can be defined as which has only one face

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Meghna Thapar 5 years ago (6237)

A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair. A function is a relation in which each input has only one output. ... : y is a function of x, x is not a function of y (y = 9 has multiple outputs). : y is not a function of x (x = 1 has multiple outputs), x is not a function of y (y = 2 has multiple outputs).

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Short notes on Political development of North East. (100 words)

Posted by Mary Engmawii 5 years, 1 month ago (9549078)

CBSE > Class 12 > Political Science

1 answers

Meghna Thapar 5 years ago (6237)

After Indian Independence from British Rule in 1947, the Northeastern region of British India consisted of Assam and the princely states of Manipur and Tripura. ... It remained the capital of undivided Assam until the formation of the state of Meghalaya in 1972. The Northeastern States are often known as the Seven Sister states because they are interdependent on one another. All these states are connected to India via Siliguri Corridor. Hence, that is the only way to reach the Seven Sister States.

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what is the important of feedback in communication?

Posted by Mohaddisha Rizvi 5 years, 1 month ago (7889825)

CBSE > Class 10 > Information Technology (402)

2 answers

Arsh Srivastava 5 years, 1 month ago (8486831)

Feedback is important in a communication because by a feedback we can understand how our language or thoughts is transferred to listener's mind...

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Kanak Tejyan 5 years, 1 month ago (10077952)

feedback includes both verbal and nonverbal communication and takes formal and informal forms formal feedback include writing comments and structured feedback while informal feedback tracks casual verbal comments and action sometimes a feedback could be a nonverbal cues such as smileys science etc while at other time it can be simply be silence shopping agreement or disagreement in in fact feedback is the receiver response which enables the sender the to evaluate the effectiveness of his/ her message I hope it helpful for you ?

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Draw the fixture for 15 teams in knockout cum league basis

Posted by Amisha Chandra 5 years, 1 month ago (10091026)

CBSE > Class 12 > Physical Education

2 answers

Ankit Kumar 5 years, 1 month ago (9651651)

You can help through CBSE guide notes or book .I

15 Thank You

Ankit Kumar 5 years, 1 month ago (9651651)

It's not possible to draw on mobile phone

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Write the purpose of blog

Posted by Kanak Tejyan 5 years, 1 month ago (10077952)

CBSE > Class 10 > Information Technology (402)

3 answers

Alok Ranjan Mahakul 5 years, 1 month ago (8627445)

Various

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Kanak Tejyan 5 years, 1 month ago (10077952)

Ok thanks ? sis

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Shreya Raj 5 years, 1 month ago (6865004)

There are various purposes for which user can have blog . some user use blog as personal.. Post about there thought and views on various topic . Some people use it as business purpose they promote and advertise there business through blog.

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Which countries had been the exporters of wine and olive oil in the later 5th and 6th centuries?

Posted by Tamanna Khandhakar 5 years, 1 month ago (10060899)

CBSE > Class 11 > History

1 answers

Yogita Ingle 5 years ago (2577571)

In the later fifth and sixth centuries, the Southern Asia Minor (Turkey), Syria and Palestine became major exporters of wine and olive oil.

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Chapter 11 ques 13 of 11.3

Posted by Raj Rai 5 years, 1 month ago (9917677)

CBSE > Class 07 > Mathematics

1 answers

Pavithra K 5 years ago (10097157)

146.9

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Why did gandhiji start non cooperation Movement explain?

Posted by Sonam Sonkar 5 years, 1 month ago (10067368)

CBSE > Class 10 > Social Science

3 answers

King?Adithya H. M.. 5 years ago (9870303)

After the suspension of the rowlatt satyagraha,Gandhiji felt the need to lauch a more broad based movement in India. ... Gandhiji convinced other leaders in the calcutta congress session of September 1920 of the need to start the non cooperation movement in support of khilafat as well as for swaraj.

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Jai Shee Ram Ok 5 years, 1 month ago (9844010)

This answer in short form write

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Meghna Thapar 4 years, 8 months ago (6237)

Gandhiji launched the Non-cooperation movement of 1921 because:
According to Gandhiji , the British rule was established in India with the cooperation of Indians, and had survived only because of this cooperation. So time has arrived o withdraw cooperation to the British.
First World War added to the misery of the Indian people. Heavy taxes, high prices, famines and epidemics made people's life miserable.
Rowlatt Act invited large scale protests throughout the country.
Jallianwala Bagh Massacre and the injustice done to Punjab made Indians angry which need to be avenged.
To restore the status of the ruler of Turkey.
To bring Swaraj or Self Rule to India.
Mahatma Gandhi declared that the main objectives of the non cooperation movement were :
To cripple the British administration and make them realize that they cannot function without the actual support of the Indians.
To avenge the wrong done by the Government in Punjab (Jallianwala Bagh Massacre) in a non violent way.
To bring about unity among the people. To inculcate a sense of nationalism.
To promote khadi and to attain Swaraj.

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What is net shown area?

Posted by Ankita Yadav 5 years, 1 month ago (9088301)

CBSE > Class 10 > Social Science

3 answers

King?Adithya H. M.. 5 years ago (9870303)

Net Area Sown: This represents the total area sown with crops and orchards. Area sown more than once in the same year is counted only once. This represents the total area sown once and/or more than once in a particular year, i.e. the area is counted as many times as there are sowings in a year.

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Yogita Ingle 5 years ago (2577571)

Net sown area is the total area sown with crops and orchards. It represents an area in which total crops are grown only once in a year.

Gross cropped area is the total area sown with crops and and orchards once or more in a year. It also include the net sown area.

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Manohar Padmanabhan 5 years, 1 month ago (9983339)

Net sown area is the total area sown with crops & orchards. It represents an area in which the total number of crops are grown only once in a year.

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