Question

in figure in the figure if angle X = angle Y AB = CB. prove that AE = CD

Answer 1

I think this would help you

Answer 2

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