Question
In a trapezium ABCD, side AB is parallel to side DC; and the diagonals AC and BD intersect each other at point P. Prove that : Δ APB is similar to Δ CPD.
✓
Answer
In ΔAPB and ΔCPD,
∠APB = ∠CPD .......(vertically opposite angles)
∠ABP = ∠CDP ....(alternate angles since AC || DC)
ΔAPB ∼ ΔCPD .....(AA criterion for similarity)
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