Question

pls can you solve I have math exam tomorrow

Answer 1

Given: AB = BC

and, x = y  

To prove: AE = CD

Proof: In ΔABE, we have,

Exterior ∠AEB = ∠EBA + ∠BAE

⇒ y = ∠EBA + ∠BAE

Again, in ΔBCD, we have

x = ∠CBA + ∠BCD

Since, x = y [Given]

So, ∠EBA + ∠BAE = ∠CBA + ∠BCD

⇒ ∠BAE = ∠BCD

Thus in ΔBCD and ΔBAE, we have

∠B = ∠B [Common]

BC = AB [Given]

and, ∠BAE = ∠BCD [Proved above]

By Angle-Side-Angle criterion of congruence, we have

ΔBCD ≅ ΔBAE

So, CD = AE [Proved by C.P.C.T.]