Important Questions CBSE Class 9 Maths Chapter 8 Quadrilaterals

Quadrilaterals are a vital topic in Class 9 Mathematics, covered in Chapter 8 of the CBSE curriculum. Mastering this topic requires understanding key concepts, theorems, and problem-solving techniques. This article presents important questions for Class 9 Maths Chapter 8 (Quadrilaterals) to help students practice and excel in their exams.

Key Concepts in Quadrilaterals

Before diving into the questions, ensure you understand these fundamental concepts:

• Types of quadrilaterals: parallelograms, rectangles, squares, rhombuses, and trapeziums.
• Properties of quadrilaterals, such as opposite sides, angles, and diagonals.
• Important theorems like the Midpoint Theorem and their applications.

Also Check: CBSE Syllabus for Class 9

Quadrilateral Class 9 Extra Questions: Very Short Answer Type Questions

Question.1 Three angles of a quadrilateral are equal and the fourth angle is equal to 144°. Find each of the equal angles of the quadrilateral.
Solution.

Question.2 Two consecutive angles of a parallelogram are (x + 60)° and (2x + 30)°. What special name can you give to this parallelogram ?
Solution.

Also Check: NCERT Solutions for Class 9

Question.3 If one angle of a parallelogram is 30° less than twice the smallest angle, then find the measure of each angle.
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Question.4 If one angle of a parallelogram is twice of its adjacent angle, find the angles of the parallelogram. [CBSE-15-6DWMW5A]
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Question.5

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Question.6.If the diagonals of a quadrilateral bisect each other at right angles, then name the quadrilateral.
Solution. Rhombus.

Also Check: NCERT Solutions for Class 9 Maths

Question.7 In quadrilateral PQRS, if ∠P = 60° and ∠Q : ∠R : ∠S = 2:3:7, then find the measure of∠S.
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Question.8 If an angle of a parallelogram is two-third of its adjacent angle, then find the smallest angle of the parallelogram.
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Question.9 In the given figure, ABCD is a parallelogram. If ∠B = 100°, then find the value of ∠A +∠C.

Solution.

Question.10 If the diagonals of a parallelogram are equal, then state its name.
Solution. Rectangle

Also Check: NCERT Solutions for Class 9 Science

Question.11 ONKA is a square with ∠KON = 45°. Determine ∠KOA.
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Question.12 PQRS is a parallelogram, in which PQ = 12 cm and its perimeter is 40 cm. Find the length of each side of the parallelogram.
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Question.13

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Question.14

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Question. 15.If ABCD is a parallelogram, then what is the measure of ∠A – ∠C ?
Solution. ∠A –∠C = 0° [opposite angles of parallelogram are equal]

Also Check: Extra Questions for Class 9 Maths with Solutions

Short Answer Questions Type-I

Question.16 Prove that a diagonal of a parallelogram divide it into two congruent triangles. [CBSE March 2012]
Solution. Given : A parallelogram ABCD and AC is its diagonal.

Question.17 ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see fig.). Show that :
(i) AAPB ≅ ACQD (ii) AP = CQ [CBSE March 2012]
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Question.18
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Question.19

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Question.20

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Question.21 If the diagonals of a parallelogram are equal, then show that it is a rectangle. [CBSE March 2012]
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Question.22 ABCD is a parallelogram and line segments AX, CY bisect the angles A and C, respectively. Show that AX\\CY. D x c
Solution.

SHORT ANSWER QUESTIONS TYPE-II

Question.23

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Question.24 ABCD is a quadrilateral in which the bisectors of ∠A and ∠C meet DC produced at Y and BA produced at X respectively. Prove that : [CBSE-15-6DWMW5A]
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Question.25 In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles. [CBSE March 2012]
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Question.26 D, E and F are respectively the mid-points of the sides AB, BC and CA of a triangle ABC. Prove that by joining these mid-points D, E and F, the triangles ABC is divided into four congruent triangles. [NCERT Exemplar Problem]
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Question.27

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Question.28

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Question.29

Solution. Since line segment joining the mid-points of two sides of a triangle is half of the third side. Therefore, D and E are mid-points of BC and AC respectively.

LONG ANSWER TYPE QUESTIONS
Question.30 ABC is a triangle right-angled at C. A line through the mid-point M of hypotenuse AB parallel to BC intersects AC ad D. Show that:
(i) D is the mid-point of AC
(ii) MD ⊥ AC
(iii) CM = MA = 1/2 AB. [CBSE March 2012]
Solution.

Question.31

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Question.32 The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it.
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Question.33

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Question.34

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Question.35 ABC is a triangle right-angled at C. A line through the mid-point M of hypotenuse AB parallel to BC intersects AC at D. Show that:
(i) D is the mid-point of AC
(ii) MD⊥ AC
(iii) CM = MA =1/2 AB. [CBSE March 2012]
Solution.

Question.36

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Question.37 ABCD is a rhombus. Show that diagonals AC bisects ∠A as well as ∠C and diagonal BD bisects∠B as well as ∠D
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Question.38

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Question.39

Solution. Here, in AABC, R and Q are the mid-points of AB and AC respectively.

Question.40

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Question.41

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Question. 42 ABCD is a parallelogram in which diagonal AC bisects∠A as well as ∠C. Show that ABCD is a rhombus. [CBSE-14-17DIG1U]
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Question. 43

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Question.44 ABCD is a parallelogram. If the bisectors DP and CP of angles D and C meet at P on side AB, then show that P is the mid-point of side AB. [CBSE-15-NS72LP7]
Solution.

Value Based Questions (Solved)

Question.1

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Question.2

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Question.3

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Class 9 Maths Chapter 8 Important Questions FAQs

What are the important questions in Chapter 8 Quadrilaterals for Class 9 CBSE?

Focus on proving properties of parallelograms, solving problems using the Midpoint Theorem, and understanding the angle sum property of quadrilaterals.

Where can I find Class 9 Maths Chapter 8 important questions?

You can access important questions for Class 9 Chapter 8 on Infinity Learn Online platform, which offer curated lists and solutions.

How to solve important questions of Quadrilaterals in Class 9 Maths?

Begin by thoroughly understanding theorems related to quadrilaterals, practice various problems, and refer to solved examples on educational websites for guidance.