Question

ABCD is a cyclic quadrilateral AB and DC are produced to meet in E. Prove that Δ EBC ∼ Δ EDA.

Answer 1

In Δ EBC and Δ EDA, we have
∠ EBC = ∠ EDA       ...[ Exterior or angle in a cyclic quadrilateral is equal to opposite interior angle]

∠ ECB = ∠ EAD       ...[ Exterior or angle in a cyclic quadrilateral is equal to opposite interior angle]
and  ∠ E = ∠ E

So, by AAA exterior of similarly, we get
Δ EBC ∼ Δ EDA 
Hence proved.