Question

Show that in an isosceles triangle angles opposite to equal sides are equal

Answer 1

Let $△ABC$ be an isosceles triangle such that AB =AC Then we have to prove that $\angle B=\angle C$ Draw the bisector AD of $\angle A$ meeting BC in D
Now in triangles ABD and ACD We have $AB=AC$ (Given)
$\angle BAD=\angle CAD$ (because AD is bisector of $\angle A$
$AD=AD$ (Common side)
Therefore by SAS congruence condition we have
$△ABC\cong △ACD$
$\Rightarrow \angle B=\angle C$
(Corresponding parts of congruent triangles are equal )