Question

State true or false:

In the figure, given below, $2AD=AB$. $P$ is mid-point of $AB$. $Q$ is mid-point of $DR$ and $PR\parallel BS$, then $DS=3RD$

• A. True
• B. False

Answer 1

The correct option is B False

Given: $PR\parallel BS$, P is mid point of AB and Q is mid point of DR
$2AD=AB$
$2AD=AP+PB$
$2AD=2AP$ (P is mid point of AB)
$AD=AP$
or A is mid point of PD
hence, $BD=3PB$
Now, In $△ABS$,
$PR\parallel BS$,
By equal intercept theorem,
$\frac{BD}{BP}=\frac{DS}{RS}$
$3=\frac{DS}{RS}$
$DS=3RS$