In the figure (1) given below, E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. show that ∆ABE ~ ∆CFB.
In the figure (1) given below, E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. show that ∆ABE ~ ∆CFB.

Solution:-

From the figure, ABCD is a parallelogram,

Then, E is a point on AD and produced and BE intersects CD at F.

We have to prove that ∆ABE ~ ∆CFB

Consider ∆ABE and ∆CFB

∠A = ∠C [opposite angles of a parallelogram]
∠ABE = ∠BFC [alternate angles are equal]
∆ABE ~ ∆CFB