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.