Theorem 8.4 Class 9 Maths Explanation with Proof

Today, we will discuss theorem 8.4 class 9 Maths which is related to Chapter 8 Quadrilaterals Class 9 Mathematics. After understanding theorem 8.4, you can solve the exercise questions given in the NCERT book of Class 9 Maths.

 

 Theorem 8.4 Class 9

In a parallelogram, opposite angles are equal.

Given 

A parallelogram ABCD.

To Prove

∠A=∠C and ∠B=∠D 

Proof 

Since ABCD is a parallelogram, therefore

AB∥DC and AD∥BC 

Now, AB∥DC and transversal AD intersects them at A and D respectively.

∴∠A+∠D=180° …………….(i)(∵sum of consecutive interior angels is 180°)

Again, AD∥BC and  DC intersect them at D and C respectively.

∴∠D+∠C=180° …………….(ii)( ∵sum of consecutive interior angels is 180°)

From (i) and (ii), we get

∠A+∠D=∠D+∠C 

⇒ ∠A=∠C 

 Similarly,  ∠B=∠D

Hence,   ∠A=∠C and ∠B=∠D  Hence Proved

Related Topics

1. Theorem 8.5

2. Theorem 8.3