Question

State true or false:

In the given figure, diagonals $PR$ and $QS$ of the parallelogram $PQRS$ intersect at point $O$ and $LM$ is parallel to $PS$, that

$2$ Area $\left(\Delta POS\right)=$ Area $\left(//gmPMLS\right)$

• A. True
• B. False

Answer 1

The correct option is A True

Given,
PQRS is a parallelogram.PR and QS intersects at O and LM is parallel to PS.
Let OO' be the altitude from O to the line PS.
$\therefore$ Area of $△POS=\frac{1}{2}\times PS\times O{O}^{\prime }$
=>2 Area $△POS=PS\times O{O}^{\prime }$
=>PS $\times$ OO'=2 Area $△POS$
=>Area of parallelogram PMLS= 2 Area $△POS$