Question

In the given figure triangle ABC is isosceles
where AB = AC and AD = AE.
Prove BE = CD.​

Answer 1

Answer: BE = CD

Step-by-step explanation:

Proof :

In the above figure ,

AB = AC and.

AD = AE. ------------->> (Given)

Consider ∆ AEB and ∆ ADC ,

AE = AD. ------------->> (Given)

angle BAE = angle CAD. ------------->> (Common

Angle)

AB = AC. ------------->> (Given)

Therefore , By S-A-S test of congruency

∆ AEB = ∆ ADC

Therefore ,

BE = CD. ------------->> ( c.s.c.t. )

Hence Proved

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{ c.s.c.t. stands for Corresponding sides of congruent triangles }

Answer 2

Answer:

Step-by-step explanation:

Given :- A triangle ABC in which AB=AC. D and E are points on BC such that BE = CD.

To prove :- AD= AE.

proof :- BE=CD

= BE-DE = CD-DE

= BD = CE

NOW IN TRIANGLE ABD AND TRIANGLE ACE,

AB=AC

ANGLE B = ANGLE C

BD = CE

BY SAS CRITERIA, TRIANGLE ABD CONGRUENT TO TRIANGLE ACE.

BY CPCT, AD = DE