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

###### Answers:

In triangle EBC and EDA, we have

∠EBC = ∠EDA [∵ Exterior angle in a cyclic quad. is equal to opposite interior angle]

∠ECB = ∠EAD [∵ Exterior angle in a cyclic quad. is equal to opposite interior angle ]

and ∠E = ∠E

so, by AAA interior of similarity, we get

ΔEBC ~ ΔEDA.

Hence proved.