Theorem 8.3 Class 9 Maths Explanation with Proof

Today, we will discuss theorem 8.3 class 9 Maths which is related to Chapter 8 Quadrilaterals Class 9 Mathematics. After understanding theorem 8.3, you can solve the exercise questions given in the NCERT book of Class 9 Maths.

 Theorem 8.3 Class 9

If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.

Given 

ABCD is a quadrilateral in which opposite sides are equal.

AB=DC and BC=AD

To Prove

ABCD is a parallelogram

AB∥DC and BC∥AD 

Construction 

Join AC

Proof

 In ∆ABC and ∆CDA

AC=AC                   (common sides)

AB=DC                  (given)

BC=AD                 (given)

∆ABC≅∆CDA     (By SSS congruence rule)

Then ∠BAC=∠ACD 

And ∠BCA=∠CAD

But these are pairs of alternate angles (By CPCT)

∴  AB∥DC and BC∥AD 

Hence ABCD is a parallelogram. Hence proved

Related Topics

1. Theorem 8.4

2. Theorem 8.2