In the given figure, AB||DC, BO=6 cm and DQ=8 cm; find the value of BP×DO.

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Solution

In △ODQ and △OPB,
∠QOD=∠BOP (Vertically opposite angles)
∠OQD=∠OPB (Alternate angles for parallel lines DQ and PB)
∠ODQ=∠OBP (Alternate angles for parallel lines DQ and PB)
Thus, △ODQ∼△OBP (AAA rule)
Hence, OD/OB=DQ/BP (Corresponding sides)
OD×BP=DQ×OB
OD×BP=6×8
OD×BP=48 cm²

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