Question

Prove that the bisector of vertical angle of an isosceles triangle is perpendicular to the base.

Answer 1

Let ABC be an isosceles triangle and in which AD besik the angle bisector of angle BAC,


then

In ∆ABD and ∆ACD, we get

AB=AC (since triangle is isosceles),.

AD=AD (common),

angle BAD=angle CAD (since AD is the angle bisector),

therefore

By SAS congruence rule,
∆ABD congruence to ∆ACD,

then
angle ADB=angle ADC,

but
angle ADB+angle ADC=180°,

then
angle ADB+angle ADB=180°,

2×angle ADB=180°,

then

angle ADB=180°/2=90°