Question

In the given fig., if <X=<Y and AB=CB, then prove that AE=CD​

Answer 1

Answer:

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 ∠BCD=∠BAE

thus angle side angle criterion of congrunce we have

ΔBCD≅ΔBAE

the corresponding parts of congruent triangle are each

so CD=AE