Question

ABCD is a cyclic quadrilateral, AB and DC are produced to meet in E. Prove that ΔEBC ≅  ΔEDA.

Answer 1

In cyclic quadrilateral ABCD ,

∠BAD + ∠ BCD = 180°  - (1)

Opposite angles of cyclic quadrilateral

Also , ∠ BCD + ∠ BCE = 180°  - (2) (Linear pair)

From (1) and (2) , we get

∠BAD = ∠BCE

In Δ EBC and Δ EDA

∠BAD = ∠BCE  (proved above)

∠ BEC = ∠ DEA  (common)

∴ Δ EBC ~ Δ EDA  (AA corollary)