Theorem 7.6 Class 9 Maths Explanation with Proof

In this post, we will discuss theorem 7.6 class 9 Maths which is related to Chapter 7 Triangles Class 9 Mathematics. After understanding theorem 7.6, you can solve the exercise questions given in the NCERT book of Class 9 Maths.

Solve Theorem 7.6 Class 9 

If two sides of a triangle are unequal, then the angle opposite to the longer side is larger.

Given 

A triangle ABC, AC>AB

To prove

∠ABC=∠BCA 

Construction

Take a point D on AC such that AD=AB. Join B and D.

Proof 

In ∆ABD

AD=AB (by construction)

∠ABD=∠BDA ………(i)

                        

                           (Angles opposite to equal sides)

∠BDA=∠BCD ………………..(ii)

(∠BDA is an exterior angle of ∆BCD and exterior angle is greater than each interior opposite angle) 

⟹    ∠ABD>∠BCD

∠ABC>∠BDA 

(since ∠ABD is a part of ∠ABC))

∠ABC>∠BCD 

Hence ∠ABC>∠BCA 

Related Topics

1. Theorem 7.5

2. Theorem 7.7