In the given figure, MNOP is a parallelogram and AB || MP. Prove that QC || PO.

MP $||$ AB
$\Rightarrow \triangle QMP \sim \triangle QAB$
$\Rightarrow \frac{MP}{AB} = \frac{QP}{QB}$ ... (i)
Now, NO $||$ MP $||$ AB
$\Rightarrow \triangle CNO \sim \triangle CAB$
$\Rightarrow \frac{NO}{AB} = \frac{CO}{CB}$ ...(ii)
As MP = NO
From (i) and (ii),
$\frac{QP}{QB} = \frac{CO}{CB}$
$\frac{QB}{QP} = \frac{CB}{CO}$
$\frac{QB}{QP} - 1 = \frac{CB}{CO} - 1$
$\frac{QB-QP}{QP} = \frac{CB-CO}{CO}$
$\frac{BP}{QP} = \frac{BO}{CO}$
or $\frac{QP}{BP} = \frac{CO}{BO}$
$\therefore$ QC $||$ PO