State true or false:

In a trapezium ABCD, side AB is parallel to side DC; and the diagonals AC and BD intersect each other at point P, then
$Δ A P B$ is similar to $Δ C P D .$

True

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False

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Solution

The correct option is A True
In $△$ APB and $△$ CPD,
$∠ A P B = ∠ C P D$ (Vertically opposite angles)
$∠ A B P = ∠ C D P$ (Alternate angles of parallel sides AB and CD)
$∠ B A P = ∠ D C P$ (Alternate angles of parallel sides AB and CD)
Hence, $△ A P B \sim △ C P D$ (AAA rule)

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