Question

Prove that if two sides of a triangle are equal, then the angles opposite those sides are equal​

Answer 1

Step-by-step explanation:

Given :

A △ABC in which ∠B=∠C.

To prove :

AB=AC

Construction :

Draw the bisector of ∠A and let it meet BC at D.

Proof  :

In △s ABD and ACD,

∠B=∠C

∠BAD=∠CAD

AD=AD

So, by AAS criterion of congruence,

△ABD≅△ACD

⟹AB=AC (by CPCT)

Answer 2

Answer:

by rhs congruency

Step-by-step explanation: we consider a triangle ABC where AB=AC and draw a perpendicular from A onto BC and name the point of intersection as D. Now considering triangles ABD and ACD,angle ADB=angle ADC=90 degrees,AD=AD common side,AB=AC(given).Therefore from rhs congruency angle ABC=angle ACD