Question

Traingle ABCD is an isosceles triangle in which AB =AC. also D is a point such that BD=CD. Prove that AD bisects Angle A Angle D.

Answer 1

Answer:angleBAD=DAC

Step-by-step explanation: coneider triangleBAD andCAD

AB=AC (isosceles triangle,given )

BD=CD( given D midpoint)

AD=AD( common )

Therefore ∆ABD~= ∆ACD (SSS)

IE ang . BAD=CAD (cpct)

Therefore AD bisects ang.A

Answer 2

Ab=ac given

In triangle. Abc

AngleB=angleC

In triangle abd and triangle acd

<b=<c

Ab=ac

Bd=cd

abd similar acd

By cpct, <bda=<cba=90

Hence proved