Question

prove that angle opposite to equal sides of an isosceles triangle are equal

Answer 1

see the attachment
hope it helps!!!

Answer 2

let ABC be an isosceles triangle and in which AD is the median on the side BC, then here we have two triangles ∆ABD and ∆ACD.


In ∆ABD and ∆ACD

AB=AC (given),

AD=AD (common),

BD=CD (since median bisect the sides),

therefore by SSS congruence rule,
∆ABD congruence to ∆ACD,

then

angel ABD=angle ACD (By C.P.C.T),


hope it's clear.....