Question

In the given figure, ABCD is a cyclic quadrilateral whose sides AB and DC are produced to meet in E. Prove that ∆EBC ∼ ∆EDA.

Answer 1

In ∆EBC and ∆EDA, we have:
Side AB of the cyclic quadrilateral ABCD is produced to E.
∠EBC = ∠CDA (Opposite angles of a cyclic quadrilateral are equal)
⇒ ∠EBC = ∠EDA ...(i)
Again, side DC of the cyclic quadrilateral ABCD is produced to E.
∠ECB = ∠BAD
∠ECB = ∠EAD ...(ii)
∠BEC = ∠DEA (Each angle equal to ∠E) ...(iii)
From (i), (ii) and (iii), we have:
∆EBC ∼ ∆EDA (AAA criterion)