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Sunday, January 29, 2023

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

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