All Solutions

Important

Friday, February 17, 2023

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

No comments:

Post a Comment