Question

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that

AD = AE, prove that BE = CD. ​

Answer 1

Step-by-step explanation:

Given ABC is an isosceles triangle with AB=AC.

Given ABC is an isosceles triangle with AB=AC.D and E are the point on BC such that BE=CD

Given AB=AC

∴∠ABD=∠ACE (opposite angle of sides of a triangle) ...(1)

Given BE=CD

Then BE-DE=CD−DE

ORBC=CE ...(2)

In ΔABD and ΔACE

∠ABD=∠ACE (From 1)

BC=CE (From 2)

AB=AC (Given)

∴ΔABD≅ΔACE

So AD=AE [cpct]

HENCE PROVED...