Question

$\Delta ABC$ is an isosceles triangle such that $AB=AC$, prove that the altitude $AD$ from $A$ on $BC$ bisects $AB$.

Answer 1

In the right triangles $ADB$ and $ADC$,
$\angle AB=\angle AC$ (Since $\Delta ABC$ is an isosceles)
$AD=DA$
Therefore, $\Delta ADB\cong \Delta ADC$ by RHS congruence condition.
So, $BD$ and $CD$ are corresponding parts of congruence triangles.