Question

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

Answer 1

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