Question

Prove that the bisector of the vertical angle of an isosceles triangle bisects the base at right angles.

Answer 1

Let $\Delta ABC$ be the isoceleus triangle with $AB=AC$ and $AD$ as vertical angle bisector

$AB=AC\angle B=\angle C\angle BAD=\angle CAD$

So by $ASA$ criteria the triangles are congruent.

$⟹BD=DC$

So the bisector of vertical angel bisects the base