Question

Prove that angles opposite to equal sides of an isosceles triangle are equal.​

Answer 1

Answer:

Angles opposite to the equal sides of an isosceles triangle are also equal. Proof: Consider an isosceles triangle ABC where AC = BC. We need to prove that the angles opposite to the sides AC and BC are equal, that is, ∠CAB = ∠CBA.Nov

Answer 2

Answer:

let there be a triangle ABC, in which AB=AC.

Construct AP bisecting angle A meeting BC at P.

to prove- angles opposite to equal sides of an isosceles triangle are equal

proof-

In ∆ABP and ∆ACP

AP=AP(common)

AB=AC(given])

angle BAP=angle CAP (by construction])

Therefore, ∆ABP congurent ∆ACP by SAS

This implies, angle ABP=angleACP by CPCT

Hence proved