Question

prove that''Angles opposites to equal sides of an isosceles triangle are equal''​

Answer 1

Let there be a triangle abc

Draw ap bisects angle a

Since ap is a bisector

There are 2 triangles formed

Let's prove that those 2 triangles are congruent

Angle bap =cap (ap bisects angle a)

Ap=ap (common side)

Ab =ac (given)

Therefore triangle abp is congruent to triangle apc

Angle abc =acp (corresponding parts of congruent triangles (cpct))

Therefore angles opposite to equal sides of an isosceles triangle are equal

Answer 2

To prove

consider triangle ABC

AB=AC

draw a perpendicular from A to BC

AB=AC

AD=AD

angle ADB=angle ADC=90

according to hypotenuse leg axiom triangles ABD,ADC are congruent

∴ angle ABD=angle ACD

Hence proved ✅