M L Aggarwal Solutions for Exercise 5: Chapter Test

In the figure given below, medians $\mathrm{BE}$ and $\mathrm{CF}$ of a $∆\mathrm{ABC}$ meet at $\mathrm{G}$. Prove that $∆\mathrm{FGE}~∆\mathrm{CGB}$

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

$\mathrm{BG}=2\mathrm{GD}$

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

In the given figure, $\mathrm{P}$ is a point on $\mathrm{AB}$ such that $\mathrm{PB}:\mathrm{AP}=3:4$ and $\mathrm{PQ}\Vert \mathrm{AC}$.
If$\mathrm{AR}\perp \mathrm{CP},\mathrm{QS}\perp \mathrm{CB}$ and $\mathrm{QS}=6 \mathrm{cm}$, calculate the length of $\mathrm{AR}$.

In a $∆\mathrm{ABC},\mathrm{D}$ and $\mathrm{E}$ are points on the sides$\mathrm{AB}$ and $\mathrm{AC}$ respectively such that $\mathrm{DE}\Vert \mathrm{BC}$. If $\mathrm{AD}=2.4 \mathrm{cm},\mathrm{AE}=3.2 \mathrm{cm},\mathrm{DE}=2 \mathrm{cm}$ and $\mathrm{BC}=5 \mathrm{cm}$, find $\mathrm{BD}$ and $\mathrm{CE}$.

In a $∆\mathrm{ABC},\mathrm{D}$ and $\mathrm{E}$ are points on the sides $\mathrm{AB}$ and $\mathrm{AC}$ respectively such that $\mathrm{AD}=5.7 \mathrm{cm},\mathrm{BD}=9.5 \mathrm{cm},\mathrm{AE}=3.3 \mathrm{cm}$ and $\mathrm{AC}=8.8 \mathrm{cm}$. Is $\mathrm{DE}\Vert \mathrm{BC}$? Justify your answer.

In the adjoining figure, $\mathrm{D}$ is a point on $\mathrm{BC}$ such that $\angle \mathrm{ABD}=\angle \mathrm{CAD}$. If $\mathrm{AB}=5 \mathrm{cm},\mathrm{AC}=3 \mathrm{cm}$ and $\mathrm{AD}=4 \mathrm{cm}$, find $\mathrm{DC}$

In the adjoining figure, the diagonals of a parallelogram intersect at $\mathrm{O}$. $\mathrm{OE}$ is drawn parallel to $\mathrm{CB}$ to meet $\mathrm{AB}$ at $\mathrm{E}$, find area of $∆\mathrm{AOE}$ : area of parallelogram $\mathrm{ABCD}$.