In the given figure, ∠EBA = ∠EAB and AC = BD. Prove that AD = BC

Given, ∠EBA =∠EAB

∴ AE = BE

[sides oppsite to equal angles are equal]

and AC = BD (given)

=>AE + EC = BE + ED

=>EC=ED[AE=BE]

In ∆ADE and ∆ BCE,

∠AED =∠BEC [vertically opposite angles]

AE = BE

ED = EC

∴AD = BC