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

Asked by suman.manoj2002 | 28th Oct, 2018, 02:33: PM

Expert Answer:

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.

Answered by Arun | 29th Oct, 2018, 11:07: AM