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Question:

E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that △ABE ≅ △CFB.

Solution:

In △ABE and △CFB, ∠ABE = ∠CFB (Alternate angles) ∠BAE = ∠BCF (opposite angles of a parallelogram) Therefore, By AA criterion of similarity, △ABE ≅ △CFB