Theorem 7.7 Class 9 Maths Explanation with Proof

In this post, we will discuss theorem 7.7 class 9 Maths which is related to Chapter 7 Triangles Class 9 Mathematics. After understanding theorem 7.7, you can solve the exercise questions given in the NCERT book of Class 9 Maths.

Solve Theorem 7.7 Class 9

If any triangle, the side opposite to the larger (greater) angle is longer.

Given

A ∆ABC, in which ∠B>∠C

To prove 

AC>AB

Proof 

In  ∆ABC, we have the following three  possibilities 

 (i) AC=AB

(ii) AC<AB

(iii) AC>AB

Out of three possibilities, one must be true

Case -1

When AC=AB

AC=AB

⇒∠B=∠C 

(∵angles opposite to equal sides of a triangle are

equal )

This is the condition with the given hypothesis that ∠B>∠C

∴AC≠AB 

Case-2

AC<AB

AC<AB

⇒∠B>∠C (∵Angles opposite to the larger side is greater)

This contradicts the given hypothesis that ∠B>∠C

∴ AC cannot be less than AB

Case-3

Now we have only one possibility AC>AB, which must be true.

Hence AC>AB 

Related Topics

1. Theorem 7.6

2. Theorem 7.8