Table of Contents

## 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.**

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

** Solution.**

** **

**Question.3 If one angle of a parallelogram is 30° less than twice the smallest angle, then find the measure of each angle.**

** Solution.**

**Question.4 If one angle of a parallelogram is twice of its adjacent angle, find the angles of the parallelogram. [CBSE-15-6DWMW5A]**

** Solution.**

**Question.5**

**Solution.**

**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.**

**Question.8 If an angle of a parallelogram is two-third of its adjacent angle, then find the smallest angle of the parallelogram.**

** Solution.**

**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

**Question.11 ONKA is a square with ∠KON = 45°. Determine ∠KOA.**

** Solution.**

**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.**

**Question.13**

**Solution.**

**Question.14**

**Solution.**

**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.

**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.**

**Question.18**

**Solution.**

**Question.19**

**Solution.**

**Question.20**

**Solution.**

**Question.21 If the diagonals of a parallelogram are equal, then show that it is a rectangle. [CBSE March 2012]**

** Solution.**

**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**

**Solution**.

**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.**

**Question.25 In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles. [CBSE March 2012]**

** Solution.**

**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.**

**Question.27**

**Solution.**

**Question.28**

**Solution.**

**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**

**Solution.**

**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.**

**Question.33**

** Solution.**

**Question.34**

**Solution.**

**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**

**Solution.**

**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.**

**Question.38**

**Solution.**

**Question.39**

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

**Question.40**

**Solution.**

**Question.41**

**Solution.**

**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.**

**Question. 43**

**Solution.**

**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**

**Solution.**

**Question.2**

**Solution.**

**Question.3**

**Solution.**