In the given figure, $T$ is the exterior point on the diagonal $PR$ of a parallelogram $PQRS$. $SR$ produced meets $OT$ at $N$ and $QR$ produced meets $ST$ at $M$. Prove that $MN\parallel SQ$.

 

In the given figure $\frac{OP}{OA}=\frac{OR}{OC}$ and $QR\parallel BC$. Prove $PQ\parallel AB$.

A girl of height $100 \mathrm{cm}$ was walking away from the base of a lamp post with a speed of $1.9 \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$. If the lamp post is of height $5 \mathrm{m}$ above the ground. Find the length of her shadow after $4 s$.

In the given figure, $XY\parallel BC$. Find the length of $YC$ in $\mathrm{cm}$.

In the given figure, $XY\parallel QR$, $\frac{PQ}{XQ}=\frac{7}{3}$ and $PR=6.3 \mathrm{cm}$. Find the value of $YR$ in $\mathrm{cm}$.

$ABCD$ is a trapezium in which $AB\parallel CD$. $P$ and $Q$ are points on sides $AD$ and $BC$ respectively such that $PQ\parallel AB$. If $PD=18 \mathrm{cm}, QC=15 \mathrm{cm}$ and $BQ=35 \mathrm{cm}$, find the value of $AD$ in $\mathrm{cm}$.

In the given figure if $\angle 1=\angle 2$ and $∆NSQ\cong ∆MTR$. Prove that $∆PTS~∆PRQ$.

In $∆ABC$ shown below, $DE\parallel BC$. If $BC=8 \mathrm{cm}$, $DE=6 \mathrm{cm}$ and area of $∆ADE=45 {\mathrm{cm}}^2$, what is the area of $∆ABC$ (in ${\mathrm{cm}}^2$)?