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Chapter 8 Class 9 Quadrilaterals

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Updated from new NCERT Books - 2023-24

Get solutions of all NCERT Questions, Exercises and Theorems of Chapter 8 Class 9 Quadrilateral free at teachoo. Answers to all questions have been solved in an easy way, with video of each and every question.

In this chapter, we will learn - 

• What is a Quadrilateral
• Angle sum property of a quadrilateral
• Different Types of Quadrilateral - Trapezium, Kite, Parallelogram, Rhombus, Rectangle, Square
• Diagonal s of a parallelogram divides it into two congruent triangles  - with Proof (Theorem 8.1)
• Opposite sides are equal in a parallelogram, and its converse  - with Proof (Theorem 8.2 and Theorem 8.3)
• Opposite angles are equal in a parallelogram, and its converse  - with Proof (Theorem 8.4 and Theorem 8.5)
• Diagonals of a parallelogram bisect each othe r, and its converse  - with Proof (Theorem 8.6 and Theorem 8.7)
• A special condition to prove parallelogram - A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel (Theorem 8.8)
• Mid-point Theorem , and its converse  - with Proof (Theorem 8.9 and Theorem 8.10)

Here, the chapter is divided into 2 parts - Concept Wise, and Serial Order Wise.

In Serial Order Wise, just like the NCERT Book - you can check exercises and examples. This is useful when you want to check a particular question.

In Concept Wise, Teachoo (टीचू) has divided the chapter into different concepts. First the concept is explained, and then the questions of that concept is done - from easy to difficult.

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Serial order wise

Concept wise.

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Assignments For Class 9 Mathematics Quadrilaterals

Assignments for Class 9 Mathematics Quadrilaterals have been developed for Standard 9 students based on the latest syllabus and textbooks applicable in CBSE, NCERT and KVS schools. Parents and students can download the full collection of class assignments for class 9 Mathematics Quadrilaterals from our website as we have provided all topic wise assignments free in PDF format which can be downloaded easily. Students are recommended to do these assignments daily by taking printouts and going through the questions and answers for Grade 9 Mathematics Quadrilaterals. You should try to do these test assignments on a daily basis so that you are able to understand the concepts and details of each chapter in your Mathematics Quadrilaterals book and get good marks in class 9 exams.

Key Concepts for Class 9 Mathematics Quadrilaterals

(1) Sum of the angles of a quadrilateral is 360 0 . (2) A diagonals of a parallelogram divides it into two congruent triangles. (3) In a parallelogram (a) diagonals bisects each other. (b) opposite angles are equal. (c) opposite sides are equal (4) Diagonals of a square bisects each other at right angles and are equal, and vice-versa. (5) A line through the mid-point of a side of a triangle parallel to another side bisects the third side. (Mid point theorem) (6) The line through the mid points of sides of a Δ ║ to third side and half of it.

Class 9 Mathematics Quadrilaterals Assignments

Class 9 mathematics quadrilaterals important questions and answers.

Question. The figures obtained by joining the mid-points of the sides of a rhombus, taken in order, is (a) a square (b) a rhombus (c) a parallelogram (d) a rectangle

a rectangle

Question. In the adjoining figure QR=RS Find ∠PSR

∠PSR = 105 0

Question. In a square ABCD, the diagonals AC and BD bisect at 0. Then Δ AOB is (a) acute angled (b) right angled (c) obtuse angled (d) equilateral

right angled

Question. Three angles of a quadrilateral are 600, 700 and 800. The fourth angle is (a) 150 0 (b) 160 0 (c) 140 0 (d) None of these

Question. ABCD is a rhombus such that ∠ACB = 400 then ∠ADB is (a) 40 0 (b) 45 0 (c) 50 0 (d) 60 0

Question. The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O, if ∠DAC = 32 0 and ∠AOB = 72 0 then is (a) 32 0 (b) 24 0 (c) 40 0 (d) 63 0

Question. A quadrilateral ABCD is a parallelogram if (a) AD || BC (b) AB = CD (c) AB = AD (d) ∠A = 60 0 , ∠C = 60 0 , ∠B = 120 0

∠A = 60 0 , ∠C = 60 0 , ∠B = 120 0

Assignments for Class 9 Mathematics Quadrilaterals as per CBSE NCERT pattern

All students studying in Grade 9 Mathematics Quadrilaterals should download the assignments provided here and use them for their daily routine practice. This will help them to get better grades in Mathematics Quadrilaterals exam for standard 9. We have made sure that all topics given in your textbook for Mathematics Quadrilaterals which is suggested in Class 9 have been covered ad we have made assignments and test papers for all topics which your teacher has been teaching in your class. All chapter wise assignments have been made by our teachers after full research of each important topic in the textbooks so that you have enough questions and their solutions to help them practice so that they are able to get full practice and understanding of all important topics. Our teachers at https://www.assignmentsbag.com have made sure that all test papers have been designed as per CBSE, NCERT and KVS syllabus and examination pattern. These question banks have been recommended in various schools and have supported many students to practice and further enhance their scores in school and have also assisted them to appear in other school level tests and examinations. Its easy to take print of thee assignments as all are available in PDF format.

Some advantages of Free Assignments for Class 9 Mathematics Quadrilaterals

• Solving Assignments for Mathematics Quadrilaterals Class 9 helps to further enhance understanding of the topics given in your text book which will help you to get better marks
• By solving one assignments given in your class by Mathematics Quadrilaterals teacher for class 9 will help you to keep in touch with the topic thus reducing dependence on last minute studies
• You will be able to understand the type of questions which are expected in your Mathematics Quadrilaterals class test
• You will be able to revise all topics given in the ebook for Class 9 Mathematics Quadrilaterals as all questions have been provided in the question banks
• NCERT Class 9 Mathematics Quadrilaterals Workbooks will surely help you to make your concepts stronger and better than anyone else in your class.
• Parents will be able to take print out of the assignments and give to their child easily.

All free Printable practice assignments are in PDF single lick download format and have been prepared by Class 9 Mathematics Quadrilaterals teachers after full study of all topics which have been given in each chapter so that the students are able to take complete benefit from the worksheets. The Chapter wise question bank and revision assignments can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 9 Mathematics Quadrilaterals Assignments PDF.

You can download free assignments for class 9 Mathematics Quadrilaterals from https://www.assignmentsbag.com

You can get free PDF downloadable assignments for Grade 9 Mathematics Quadrilaterals from our website which has been developed by teachers after doing extensive research in each topic.

On our website we have provided assignments for all subjects in Grade 9, all topic wise test sheets have been provided in a logical manner so that you can scroll through the topics and download the worksheet that you want.

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• Quadrilaterals

Class 9 NCERT (CBSE and ICSE) Quadrilaterals

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Unit 11: Quadrilaterals

• Polygons as special curves (Opens a modal)
• Open and closed curves Get 3 of 4 questions to level up!
• Polygon types Get 3 of 4 questions to level up!

Angle sum property

• Sum of interior angles of a polygon (Opens a modal)
• Sum of the exterior angles of a polygon (Opens a modal)
• Angles of a polygon Get 3 of 4 questions to level up!
• Interior and exterior angles of a polygon Get 3 of 4 questions to level up!

Kinds of quadrilaterals

• Intro to quadrilateral (Opens a modal)
• Quadrilateral types (Opens a modal)
• Kites as a geometric shape (Opens a modal)
• Analyze quadrilaterals Get 3 of 4 questions to level up!
• Quadrilateral types Get 3 of 4 questions to level up!

Properties of a parallelogram

• Proof: Opposite sides of a parallelogram (Opens a modal)
• Proof: Opposite angles of a parallelogram (Opens a modal)
• Proof: Diagonals of a parallelogram (Opens a modal)
• Proof: Rhombus diagonals are perpendicular bisectors (Opens a modal)
• Rhombus diagonals (Opens a modal)
• Side and angle properties of a parallelogram (level 1) Get 3 of 4 questions to level up!
• Side and angle properties of a parallelogram (level 2) Get 3 of 4 questions to level up!
• Diagonal properties of parallelogram Get 3 of 4 questions to level up!

• Class 9 Maths MCQs
• Chapter 8 Quadrilaterals Mcq

Class 9 Maths Chapter 8 Quadrilaterals MCQs

Class 9 Maths Chapter 8 Quadrilaterals MCQs are available here with answers, online. The questions are prepared, as per the CBSE syllabus and NCERT curriculum. Students can prepare for exams with the help of these objective questions to score good marks. The answers are available with detailed explanations. Get chapter-wise MCQs at BYJU’S and also check Important Questions for Class 9 Maths .

To get more MCQs on Class 9 Maths Chapter 8, click on the below link.

Class 9 Maths Chapter 8 Quadrilaterals MCQs – Practice Questions

MCQs on Class 9 Maths Chapter 8 Quadrilaterals

Solve the questions provided below with four multiple options and choose the correct one.

1) The quadrilateral whose all its sides are equal and angles are equal to 90 degrees, it is called:

a. Rectangle

d. Parallelogram

2) The sum of all the angles of a quadrilateral is equal to:

3) A trapezium has:

a. One pair of opposite sides parallel

b. Two pairs of opposite sides parallel to each other

c. All its sides are equal

d. All angles are equal

Explanation: A trapezium has only one pair of opposite sides parallel to each other, and the other two sides are non-parallel.

4) A rhombus can be a:

a. Parallelogram

b. Trapezium

5) A diagonal of a parallelogram divides it into two congruent:

b. Parallelogram

c. Triangles

d. Rectangle

6) In a parallelogram, opposite angles are:

c. Cannot be determined

d. None of the above

7) The diagonals of a parallelogram:

c. Bisect each other

d. Have no relation

8) Each angle of the rectangle is:

a. More than 90°

b. Less than 90°

c. Equal to 90°

d. Equal to 45°

Explanation: Let ABCD is a rectangle, and ∠A = 90°

AD || BC and AB is a transversal

∠ A + ∠ B = 180° (Interior angles on the same side of the transversal)

So, ∠ B = 180° – ∠ A = 180° – 90° = 90°

Now, ∠ C = ∠ A and ∠ D = ∠ B (Opposite angles of the parallelogram)

So, ∠ C = 90° and ∠ D = 90°

Hence all sides are equals to 90°.

9) The angles of a quadrilateral are in the ratio 4: 5: 10: 11. The angles are:

a. 36°, 60°, 108°, 156°

b. 48°, 60°, 120°, 132°

c. 52°, 60°, 122°, 126°

d. 60°, 60°, 120°, 120°

Explanation: Let x be the common angle among all the four angles of a quadrilateral.

As per angle sum property, we know:

4x+5x+10x+11x = 360°

Hence, angles are

4x = 4 (12) = 48°

5x = 5 (12) = 60°

10x = 10 (12) = 120°

11x = 11 (12) = 132°

10) If ABCD is a trapezium in which AB || CD and AD = BC, then:

b. ∠A > ∠B

c. ∠A < ∠B

Explanation: Draw a line through C parallel to DA intersecting AB produced at E.

CE = AD (Opposite sides)

AD = BC (Given)

⇒ ∠CBE = ∠CEB

∠A + ∠CBE = 180° (Angles on the same side of transversal and ∠CBE = ∠CEB)

∠B + ∠CBE = 180° ( As Linear pair)

11) Which of the following is not true for a parallelogram?

(a) Opposite sides are equal

(b) Opposite angles are equal

(c) Opposite angles are bisected by the diagonals

(d) Diagonals bisect each other.

Explanation: Opposite angles are bisected by the diagonals is not true for a parallelogram. Whereas opposite sides are equal, opposite angles are equals, diagonals bisect each other are the properties of a parallelogram.

12) Three angles of a quadrilateral are 75º, 90º and 75º. The fourth angle is

Explanation: We know that the sum of angles of a quadrilateral is 360º.

Let the unknown angle be x.

Therefore, 75º+90º+75º+x = 360º

x = 360º – 240º = 120º.

13) ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is

Explanation: We know that the diagonals of the rhombus bisect each other perpendicularly.

By using the alternate interior angles, and angle sum property of triangle, we can say:

From the triangle, BOC,

∠BOC + ∠OCB + ∠OBC = 180º

(where  ∠BOC= 90º, ∠OCB = 40º)

90º+40º+ ∠OBC = 180º

∠OBC = 180º – 130º

Now, by using alternate angles, we can say

14) The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rhombus, if

(a) PQRS is a rhombus

(b) PQRS is a parallelogram

(c) Diagonals of PQRS are perpendicular

(d) Diagonals of PQRS are equal.

Explanation: The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rhombus if the diagonals of PQRS are equal.

15) A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is

Explanation: Consider the rectangle ABCD

In a triangle BOC, 

∠OBC = ∠OCB (Opposite angles of isosceles triangle)

Therefore, ∠OBC + ∠OCB+∠BOC = 180º

25º+25º + ∠BOC = 180º

∠BOC = 180º- 50º

∠BOC = 130º.

By using the linear pair, 

∠AOB + ∠BOC = 180º

∠AOB = 180º – 130º

Hence, the acute angle between the diagonals is 50º.

16) If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4, then ABCD is a

(b) Rhombus

(c) Parallelogram

(d) Trapezium

Explanation: 

Given that, the angles A, B, C and D of a quadrilateral are in the ratio 3:7:6:4.

We know that A+B+C+D = 360º

Hence, now we can assume, 3k+7k+6k+4k= 360º

Therefore, A = 3k = 54º

B= 7k = 126º

C = 6k = 108º

D = 4k= 72º

If we draw the quadrilateral with these angles, we get a trapezium.

17) The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if

(a) PQRS is a rectangle

(d) Diagonals of PQRS are equal

Explanation: The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if the diagonals of PQRS are perpendicular.

18) The figure obtained by joining the mid-points of the sides of a rhombus, taken in order, is

(a) a square

(b) a rhombus

(c) a rectangle

(d) any parallelogram

Explanation: Let ABCD be a rhombus. P, Q, R, S be the midpoint of the sides AB, BC, CD and DA. If we join the midpoints, we will get the shape rectangle.

19) If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form

(b) Rectangle

(c) Rhombus

(d) any other parallelogram

Explanation:

Hence, the bisectors of the angles APQ, BPQ, CQP and PQD form the shape rectangle.

20) Which of the following is not a quadrilateral?

(c) Triangle

(d) Rhombus

Explanation: square, kite and rhombus are quadrilaterals as it has four sides. Whereas a triangle is not a quadrilateral as it has only three sides.

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