Theorem 6.8 Class 9 Maths Explanation with Proof

Theorem 6.8 Class 9 Maths Explanation with Proof

In this post, we will discuss theorem 6.8 class 9 Maths which is related to Chapter 6 Lines and Angles Class 9 Mathematics. After understanding theorem 6.8, you can solve the exercise questions given in the NCERT book of Class 9 Maths.

Theorem 6.8 Class 9 maths

If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

Given 

A   ∆ABC  in which side BC is produced to D to form the exterior ∠ACD.

To prove 

∠A+∠B =∠ACD

Proof

In  ∠ABC,

∠A+∠B+∠ACB=180° (by angle sum property of a triangle)……..(i)

Here,BCD is a straight line 

∴   ∠ACB+∠ACD=180° ……..(ii)

From equations (i) and (ii)

∠A+∠B+∠ACB=∠ACB+∠ACD

∠A+∠B=∠ACD

Hence proved 

Related Topics for You

1.    Next theorem – Theorem 6.1 Class 9 Maths

2.    Previous theorem –Theorem 6.7 Class 9 Maths

3.     NCERT Solution of Exercise  6.2