Question

Z 10) In AABC, AB = AC. BC is extended on both sides
to Eand D respectively such that CE = BD.
Prove that AD = AE.
A
D B.
СЕ​

Answer 1

$\huge \underbrace \mathfrak \red{Answer ⤵}$

AB=AC(isoscelestriangleABC)→(i)

EC=BD(given)

⇒EB+BC=BC+CD⇒EB=CD→(ii)

∠ABC=∠ACB(isoscelestriangleABC)

180−∠ABC=180=∠ACB⇒∠ABE=ACD→(iii)

fromequation(i),(ii),(iii)

ΔABE≅ΔACD

byCPCT

AE=AD hence proved.

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