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E is a point ...

Question

$E$ is a point on the side $A D$ produced of a parallelogram ABCD and $B E$ intersects $C D$ at $F .$ Show that $△ A B E \sim △ C F B$ .

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Solution

In $△ A B E$ and $△ C F B,$
$∠ A B E = ∠ C F B$ (Alternate angles)
$∠ B A E = ∠ B C F$ (opposite angles of a parallelogram)
$∴$ By AA criterion of similarity, $△ A B E$ $\sim$ $△ C F B$

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