Question

In an isosceles triangle ABC with AB=AC and E are two points on BC such that BE=CD. show that AD= AE​

Answer 1

GIVEN:

A ∆ ABC in which AB=AC. D and E are points on BC such that BE=CD.

TO PROVE:

AD=AE.

PROOF:

BE=CD (given)

BE - DE=CD -DE

BD=CE. ......... equation(I)

Now , in ∆ABD and ∆ACE, we have

AB=AC. (given),

angle B = angle C. [angles opposite to

equal sides]

and BD=CE [proved above in (I)]

.

. . ∆ ABD concurrent ∆ ACE

(SAS criteria).

hence,

AD=AE. (by c.p.c.t)

HENCE. PROVED.