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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