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Important Questions for CBSE Class 9 Mathematics Quadrilaterals

October 11, 2018 by Sastry CBSE

Important Questions for CBSE Class 9 Mathematics Chapter 2 Quadrilaterals

The topics and sub-topics in Class 9 Maths Chapter 8 Quadrilaterals:

  • Quadrilaterals
  • Introduction
  • Angle Sum Property Of A Quadrilateral
  • Types Of Quadrilaterals
  • Properties Of A Parallelogram
  • Another Condition For A Quadrilateral To Be A Parallelogram
  • The MidPoint Theorem
  • Summary

IMPORTANT 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.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-1

Question.2 Two consecutive angles of a parallelogram are (x + 60)° and (2x + 30)°. What special name can you give to this parallelogram ?
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-2

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Question.3 If one angle of a parallelogram is 30° less than twice the smallest angle, then find the measure of each angle.
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-3

Question.4 If one angle of a parallelogram is twice of its adjacent angle, find the angles of the parallelogram. [CBSE-15-6DWMW5A]
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-4

Question.5
important-questions-for-cbse-class-9-mathematics-quadrilaterals-5
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-6

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

Question.7 In quadrilateral PQRS, if ∠P = 60° and ∠Q : ∠R : ∠S = 2:3:7, then find the measure of∠S.
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-7
important-questions-for-cbse-class-9-mathematics-quadrilaterals-8

Question.8 If an angle of a parallelogram is two-third of its adjacent angle, then find the smallest angle of the parallelogram.
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-9

Question.9 In the given figure, ABCD is a parallelogram. If ∠B = 100°, then find the value of ∠A +∠C.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-10
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-11

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

Question.11 ONKA is a square with ∠KON = 45°. Determine ∠KOA.
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-12

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.
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-13

Question.13
important-questions-for-cbse-class-9-mathematics-quadrilaterals-14
Solution.
cbse-class-9-mathematics-quadrilaterals-79

Question.14
cbse-class-9-mathematics-quadrilaterals-80
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-15

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]

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.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-16

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]
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-17

Question.18
important-questions-for-cbse-class-9-mathematics-quadrilaterals-18
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-19

Question.19
important-questions-for-cbse-class-9-mathematics-quadrilaterals-20
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-21

Question.20
important-questions-for-cbse-class-9-mathematics-quadrilaterals-22
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-23

Question.21 If the diagonals of a parallelogram are equal, then show that it is a rectangle. [CBSE March 2012]
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-24
important-questions-for-cbse-class-9-mathematics-quadrilaterals-25

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.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-26

SHORT ANSWER QUESTIONS TYPE-II
Question.23
important-questions-for-cbse-class-9-mathematics-quadrilaterals-27
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-28
important-questions-for-cbse-class-9-mathematics-quadrilaterals-29

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]
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-30
important-questions-for-cbse-class-9-mathematics-quadrilaterals-31

Question.25 In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles. [CBSE March 2012]
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-32

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]
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-33

Question.27
important-questions-for-cbse-class-9-mathematics-quadrilaterals-34
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-35

Question.28
important-questions-for-cbse-class-9-mathematics-quadrilaterals-36
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-37

Question.29
important-questions-for-cbse-class-9-mathematics-quadrilaterals-38
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.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-39

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.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-40
important-questions-for-cbse-class-9-mathematics-quadrilaterals-41

Question.31
important-questions-for-cbse-class-9-mathematics-quadrilaterals-42
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-43

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.
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-44
important-questions-for-cbse-class-9-mathematics-quadrilaterals-45

Question.33
important-questions-for-cbse-class-9-mathematics-quadrilaterals-46
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-47

Question.34
important-questions-for-cbse-class-9-mathematics-quadrilaterals-48
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-49
important-questions-for-cbse-class-9-mathematics-quadrilaterals-50
important-questions-for-cbse-class-9-mathematics-quadrilaterals-51

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.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-52

Question.36
important-questions-for-cbse-class-9-mathematics-quadrilaterals-53
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-54
important-questions-for-cbse-class-9-mathematics-quadrilaterals-55

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
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-56

Question.38
important-questions-for-cbse-class-9-mathematics-quadrilaterals-57
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-58
important-questions-for-cbse-class-9-mathematics-quadrilaterals-59

Question.39
important-questions-for-cbse-class-9-mathematics-quadrilaterals-60
Solution. Here, in AABC, R and Q are the mid-points of AB and AC respectively.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-61

Question.40
important-questions-for-cbse-class-9-mathematics-quadrilaterals-62
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-63

Question.41
important-questions-for-cbse-class-9-mathematics-quadrilaterals-64
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-65
important-questions-for-cbse-class-9-mathematics-quadrilaterals-66

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]
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-67

Question. 43
important-questions-for-cbse-class-9-mathematics-quadrilaterals-68
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-69
important-questions-for-cbse-class-9-mathematics-quadrilaterals-70

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.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-71

Value Based Questions (Solved)

Question.1
important-questions-for-cbse-class-9-mathematics-quadrilaterals-72
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-73

Question.2
important-questions-for-cbse-class-9-mathematics-quadrilaterals-74
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-75

Question.3
important-questions-for-cbse-class-9-mathematics-quadrilaterals-76
Solution.
important-questions-for-cbse-class-9-mathematics-quadrilaterals-77
important-questions-for-cbse-class-9-mathematics-quadrilaterals-78

NCERT Solutions for Class 9 Maths

  1. Chapter 1 Number systems
  2. Chapter 2 Polynomials
  3. Chapter 3 Coordinate Geometry
  4. Chapter 4 Linear Equations in Two Variables
  5. Chapter 5 Introduction to Euclid Geometry
  6. Chapter 6 Lines and Angles
  7. Chapter 7 Triangles
  8. Chapter 8 Quadrilaterals
  9. Chapter 9 Areas of Parallelograms and Triangles
  10. Chapter 10 Circles
  11. Chapter 11 Constructions
  12. Chapter 12 Heron’s Formula
  13. Chapter 13 Surface Areas and Volumes
  14. Chapter 14 Statistics
  15. Chapter 15 Probability
  16. Class 9 Maths (Download PDF)

Filed Under: CBSE Tagged With: CBSE 9 Quadrilaterals, CBSE Class 9, CBSE Important Questions for Class 9 Mathematics

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