Question

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

Answer 1

There's a theroem that states that if two sides of a triangle are congruent , then the angles opposite these sides are also congruent
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Answer 2

Take triangle ABC, AB=BC
Draw median D from A on BC
In triangle ABD and ACD
AB=AC
BD=DC(Construction)
AD=AD
So triangle ABD is congruent to ACD
So angle B is equal to angle C(CPCT)