Through the mid-point $\mathrm{M}$ of the side $\mathrm{CD}$ of a parallelogram $\mathrm{ABCD},$ the line $\mathrm{BM}$ is drawn intersecting diagonal $\mathrm{AC}$ in $\mathrm{L}$ and $\mathrm{AD}$ produced in $\mathrm{E}.$ Prove that : $\mathrm{El}=2\mathrm{BL}.$

In the given figure, $\mathrm{P}$ is a point on $\mathrm{AB}$ such that $\mathrm{AP}:\mathrm{PB}=4:3.$ $\mathrm{PQ}$ is parallelogram to $\mathrm{AC}.$

Calculate the ratio $\mathrm{PQ}:\mathrm{AC},$ giving reason for your answer.

In the given figure, $\mathrm{P}$ is a point on $\mathrm{AB}$ such that $\mathrm{AP}:\mathrm{PB}=4:3.$ $\mathrm{PQ}$ is parallel to $\mathrm{AC}.$

In triangle $\mathrm{ARC}, \angle \mathrm{ARC}=90º$ and in triangle $\mathrm{PQS}, \angle \mathrm{PSQ}=90º.$ Given $\mathrm{QS}=6\mathrm{cm},$ calculate the length of $\mathrm{AR}.$

In the right-angled triangle $\mathrm{QPR}, \mathrm{PM}$ is an altitude.

Given that $\mathrm{QR}=8\mathrm{cm}$ and $\mathrm{MQ}=3.5\mathrm{cm},$ calculate the value of $\mathrm{PR}.$

In the figure, given below, the medians $\mathrm{BD}$ and $\mathrm{CE}$ of a triangle $\mathrm{ABC}$ meet at $\mathrm{G}.$ Prove that : $∆\mathrm{EGD}~∆\mathrm{CGB}$

In the figure, given below, the medians $\mathrm{BD}$ and $\mathrm{CE}$ of a triangle $\mathrm{ABC}$ meet at $\mathrm{G}.$ Prove that :

$\mathrm{BG}=2 \mathrm{GD}$ from $\left(\mathrm{i}\right)$ above.

In the following figure, point $\mathrm{D}$ divides $\mathrm{AB}$ in the ratio $3:5.$ Find: $\frac{\mathrm{AE}}{\mathrm{EC}}$

In the following figure, point $\mathrm{D}$ divides $\mathrm{AB}$ in the ratio $3:5.$ Find :

$\frac{\mathrm{AD}}{\mathrm{AB}}$

In the following figure, point $\mathrm{D}$ divides $\mathrm{AB}$ in the ratio $3:5.$ Find:

$\frac{\mathrm{AE}}{\mathrm{AC}}$