Question

prove that the bisector of the Vertical angle of an isosceles triangle is perpendicular to the base​

Answer 1

Let in triangle ABC,AD is bisector of vertical angle.

In ∆ABD and ∆ACD

AB=BC

angle BAD=angle CAD

AD is common line.

By SAS congruency ∆ABD congruent to ∆CBD

So,

angle ADB=angle ADC

let angle ADB=x.

so angle ADC=x.

x+x=180

2x=180

x=90

Hence it's proved.