# NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals: Many shapes around us are in the form of quadrilaterals. Such as top of a table, paper, wall, roof etc. So studying about properties of different types of quadrilaterals is necessary. The NCERT Solutions for Class 9 Maths Chapter 8 we will study about parallelogram and their properties. A quadrilateral with parallel opposite sides is a parallelogram. After the introduction, the NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals starts with recollecting the angle sum property of a quadrilateral. That is the sum of angles of a quadrilateral is 360 degrees. This is obtained by dividing the quadrilateral into two triangles by drawing a diagonal. We know that the sum of angles of a triangle is 180 degrees. So the sum of angles of the two triangles will be 360 degrees.

The next topic this chapter of NCERT Solutions for Class 9 Maths talks briefly about different types of quadrilaterals. And finally, the NCERT Solutions of this chapter introduces different properties of the parallelogram and the midpoint theorem. This chapter of NCERT Solutions for Class 9 contains two exercises. The first exercise is related to the properties of parallelogram and second exercise focus on midpoint theorem along with the properties of a parallelogram.

The main topics of NCERT Solutions for Class 9 Maths Chapter 8 are given below

8.1 Introduction

8.2Angle Sum Property of a Quadrilateral

8.4 Properties of a Parallelogram

8.5 Another Condition for a Quadrilateral to be a Parallelogram

8.6 The Mid-point Theorem

Below is the list of properties mentioned in the NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals:

1. The diagonal of a parallelogram divides it into two congruent triangles

In figure 1 parallelogram ABCD, the diagonal AC divides it into two congruent triangles ABC and CDA

2.  Opposite sides of a parallelogram are equal. That is in figure 1 AD=BC and AB=DC

3.  If each pair of opposite sides of a quadrilateral are equal then it is a parallelogram. That is in figure 1 if AD=BC and AB=DC then ABCD is a parallelogram

4.  In a parallelogram opposite angles are equal. That is angle A = angle C and angle D = angle B

5.  If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.

6. Diagonals of a parallelogram bisect each other

7. If diagonals of a quadrilateral bisect each other then it is a parallelogram

The properties 5 says that in a parallelogram ABCD as in figure 2 if AC and BD are diagonals and if diagonals intersect at O then AO=OC and OD=OB and property 6 says that if AO=OC and OD=OB then ABCD is a parallelogram.

8. In a quadrilateral, if a pair of sides are equal and parallel then it is a parallelogram

Another topic mentioned in the NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals is the midpoint theorem. The midpoint theorems are listed below

9. The line segment joining the mid-points of two sides of a triangle is parallel to the third side

10. The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side.

The theorem 9 says that if E and F are the midpoint of sides AB and AC respectively as shown in figure 3 then EF is parallel to BC and the theorem 10 says that EF= 0.5 BC

## NCERT Solutions for Class 9 Maths - Chapter Wise

 Chapter No. Chapter Name Chapter 1 Number Systems Chapter 2 Polynomials Chapter 3 Coordinate Geometry Chapter 4 Linear Equations In Two Variables Chapter 5 Introduction to Euclid's Geometry Chapter 6 Lines And Angles Chapter 7 Triangles Chapter 9 Areas of Parallelograms and Triangles Chapter 10 Circles Chapter 11 Constructions Chapter 12 Heron’s Formula Chapter 13 Surface Areas and Volumes Chapter 14 Statistics Chapter 15 Probability