Question

In the given figure, AD=AE and angle BAD=angle CAE. Prove that AB=AC.​

Answer 1

Answer:

angle AD=AE

Angle BAD=CAE

Prove=AB=AC

AD=AB

AE=AC

hence proved=

AB=AC

Answer 2

Given :- In fig :

AC = AE, AB= AD

& angle BAD = angle EAC

To prove :- BC = DE

Proof :- angle 1 = angle 2 (given)

Add angle 3 on both the sides

--> angle 1 + angle 3 = angle 2 + angle 3

or , angle BAC = angle DAC --------1.

Now , In triangle ABC and driangle ADE

angle BAC = angle DAE ( from 1.)

AB = AD (given)

AC = AE (given)

Therefore , triangle ABC congruent to triangle ADE (SAS).

Therefore, BC = DE (cpct)