Question

The angles opposite to equal sides of an isosceles triangle are _______.

Answer 1

Consider an isosceles triangle $\Delta ABC$ with equal sides AB and AC as shown in the following figure.

Construction: AD is a bisector of $\angle A$.
In $\Delta ABD$ and $\Delta ACD$
$AB=AC$ as given.
$\angle BAD=\angle DAC$
$AD=AD$ [Common side]
Thus, By SAS, we say that $\Delta ABD\cong \Delta ACD$
Therefore, $\angle ABD=\angle ACD$
Hence, the angles opposite to equal sides of an isosceles triangle are equal.