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

In ΔDOQ and ΔBOP,

As AB || DC so, PB || DQ and BD is transversal.

∴ ∠QDO = ∠PBO [Alternate angles]

∠DOQ = ∠BOP [Vertically opposite angles are equal]

Hence, ∆DOQ ~ ∆BOP [By AA]

Since, corresponding sides of similar triangles are proportional we have :

$\Rightarrow \dfrac{DO}{BO} = \dfrac{DQ}{BP} \\[1em] \Rightarrow \dfrac{DO}{6} = \dfrac{8}{BP} \\[1em] \Rightarrow BP \times DO = 8 \times 6 = 48 \text{ cm}^2. \\[1em]$

Hence, BP x DO = 48 cm².