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