Question

In the given figure, AE = DE, CE = BE, then prove that AB = CD.

Answer 1

Answer:

In triangle AEB and triangle CED

AE=DE

BE=CE

angle AEB=angle CED

therefore triangle AED is congruence to triangle CDE

then AB=CD(CPCT).

Answer 2

Answer:

It is congruent by ASA congruent condition

hence, AB=CD

Explanation:

in triangle ABD & CBD

adding AE +DE = CE +BE

AD=CB

now,

AD=CB ( proved above)

angle B = angle D

BD=DB (common)

so by asa congruence condition the triangle ABD is congruent to triangle CBD

Hence, AB=CD (c.p.c.t )