Important Questions for CBSE Class 9 Mathematics Quadrilaterals

Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals

Quadrilateral Class 9 Extra Questions CBSE 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
Class 9 Quadrilaterals Extra Questions CBSE 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 Class 9 Mathematics Chapter 8 Quadrilaterals 1

Questions On Quadrilaterals For Class 9 CBSE 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 Class 9 Mathematics Chapter 8 Quadrilaterals 2

Extra Questions For Class 9 Maths Quadrilaterals With Solutions More Resources for CBSE Class 9

Class 9 Maths Quadrilaterals Extra Questions CBSE 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 Class 9 Mathematics Chapter 8 Quadrilaterals 3

Quadrilateral Class 9 Worksheet With Answers CBSE 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 Class 9 Mathematics Chapter 8 Quadrilaterals 4

Extra Questions On Quadrilaterals Class 9 CBSE Question.5
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 5
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 6

Quadrilateral Questions And Answers CBSE 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 Class 9 Mathematics Chapter 8 Quadrilaterals 7
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 8

Quadrilateral Questions And Answers For Class 9 CBSE 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 Class 9 Mathematics Chapter 8 Quadrilaterals 9

Quadrilateral Class 9 Questions CBSE Question.9 In the given figure, ABCD is a parallelogram. If ∠B = 100°, then find the value of ∠A +∠C.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 10
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 11

Quadrilaterals Class 9 Extra Questions With Solutions CBSE 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 Class 9 Mathematics Chapter 8 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 Class 9 Mathematics Chapter 8 Quadrilaterals 13

Question.13
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 14
Solution.
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Question.14
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Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 17

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 Class 9 Mathematics Chapter 8 Quadrilaterals 18

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 Class 9 Mathematics Chapter 8 Quadrilaterals 19

Question.18
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Solution.
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Question.19
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Solution.
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Question.20
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Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 25

Question.21 If the diagonals of a parallelogram are equal, then show that it is a rectangle. [CBSE March 2012]
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 26
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 27

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 Class 9 Mathematics Chapter 8 Quadrilaterals 28

SHORT ANSWER QUESTIONS TYPE-II
Question.23
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 29
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 30
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 31

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 Class 9 Mathematics Chapter 8 Quadrilaterals 32
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 33

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 Class 9 Mathematics Chapter 8 Quadrilaterals 34

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 Class 9 Mathematics Chapter 8 Quadrilaterals 35

Question.27
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 36
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 37

Question.28
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 38
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 39

Question.29
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 40
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 Class 9 Mathematics Chapter 8 Quadrilaterals 41

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 Class 9 Mathematics Chapter 8 Quadrilaterals 42
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 43

Question.31
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 44
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 45

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 Class 9 Mathematics Chapter 8 Quadrilaterals 46
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 47

Question.33
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 48
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 49

Question.34
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 50
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 51
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 52
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 53

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 Class 9 Mathematics Chapter 8 Quadrilaterals 54

Question.36
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 55
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 56
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 57

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 Class 9 Mathematics Chapter 8 Quadrilaterals 58

Question.38
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 59
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 60
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 61

Question.39
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 62
Solution. Here, in AABC, R and Q are the mid-points of AB and AC respectively.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 63

Question.40
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 64
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 65

Question.41
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 66
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 67
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 68

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 Class 9 Mathematics Chapter 8 Quadrilaterals 69

Question. 43
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 70
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 71
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 72

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 Class 9 Mathematics Chapter 8 Quadrilaterals 73

Value Based Questions (Solved)

Question.1
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 74
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 75

Question.2
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 76
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 77

Question.3
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 78
Solution.
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 79
Important Questions for Class 9 Mathematics Chapter 8 Quadrilaterals 80