Question

The perpendicular from a vertex of an isosceles triangle bisects the base and and the vertex angle. (True/False)

Answer 1

Here, in the iscosceles triangle ABC,
$AB=AC$
$\angle ADC=\angle ADB={90}^o$
Side AD is common
Hence, $△ADC\cong △ADB$

We now, corresponding sides and angles os congruent triangles are equal.
Hence, $BD=CD$
$\angle BAD=\angle CAD$=
Hence, altitude AD of the isosceles triangle is also a median and angle bisector.