Question

In the given isosceles triangle 𝐀𝐁𝐂 with 𝐀𝐁 = 𝐀𝐂, 𝐃 and 𝐄 are points on 𝐁𝐂 such that 𝐁𝐄 = 𝐂𝐃. Show that 𝐀𝐃 = 𝐀𝐄.

Answer 1

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

BD = CE......................................(2)

In ΔABD and ΔACE

∠ABD = ∠ACE ( From 1 )

BD = CE ( from 2 )

AB = AC ( Given )

∴ΔABD≅ΔACE

So AD = AE [ hence proved ]