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Question
In the given figure, AB || DC, BO = 6 cm and DQ = 8 cm; find: BP × DO.
Solution
In ΔDOQ and ΔBOP,
∠QDO = ∠PBO ...(Since AB || DC that is, PB || DQ)
So, ∠DOQ = ∠BOP ...(Vertically opposite angles)
`=>` ΔDOQ ∼ ΔBOP ...(AA criterion for similarity)
`=> (DO)/(BO) = (DQ)/(BP)`
`=> (DO)/6 = 8/(BP)`
`=>` BP × DO = 8 × 6 = 48 cm2
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