1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# 3 mark question Prove side opposite to greater angle is longer in a triangle.

Open in App
Solution

## Theorem : if in a triangle two angles are not equal, then the side opposite to the greater angle is longer than the side opposite to the smaller angle. given: let ABC be a triangle in which the angle ABC is greater than the angle ACB. TPT: AC > AB proof: let us try to prove this by contradiction. let us assume that AC is not longer than AB. then two cases will arise: case I : AC = AB case II : AC < AB if AC = AB. triangle ABC would has been isosceles triangle and angle ABC = angle BAC this contradicts to the given condition. in the II nd case: the side BC would has been longer than AC and consequently the. angle ABC < angle BAC. but from the theorem " If in a triangle two sides are un equal , then angle opposite to longer side is greater than the angle opposite to shorter side". again this contradicts the given condition. thus the only remaining possibility is that the side AC is longer than the side BC. thus AC > AB

Suggest Corrections
11
Join BYJU'S Learning Program
Related Videos
"If Two Sides of a Triangle are Unequal, Then the Angle Opposite to the Greater Side is Greater
MATHEMATICS
Watch in App
Join BYJU'S Learning Program