# <span lang="EN-US

Given: x=y and AB=CB

To prove: AE = CD

Proof:

In ∆ABE, we have,

AEC = EBA + BAE …Exterior angle theorem

y° = EBA + BAE

Now in ∆BCD, we have,

x° = CBA + BCD

Since, given that,

x = y ,

CBA + BCD = EBA + BAE

BCD = BAE … as CBA and EBA and same angles.

Hence in ∆BCD and ∆BAE,

B = B

BC = AB …given

BCD = BAE

Thus by ASA property of congruence, we have,

∆BCD BAE

Hence, we know that, corresponding parts of the congruent triangles are equal

CD = AE

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