M L Aggarwal Solutions for Exercise 2: Exercise 13.2

$E$ and $F$ are points on the sides $PQ$ and $PR$ respectively of a $△PQR$. For the following case, state whether $EF\parallel QR$:

$PE=3.9 \mathrm{cm}, \mathrm{EQ}=3 \mathrm{cm}, \mathrm{PF}=8 \mathrm{cm} \mathrm{and} \mathrm{RF}=9 \mathrm{cm}$.

In $△\mathrm{PQR}$, $\mathrm{E}$ and $\mathrm{F}$ are points on the sides $\mathrm{PQ}$ and $\mathrm{PR}$ respectively. Then for the given condition as$\mathrm{PQ}=1.28 \mathrm{cm}, \mathrm{PR}=2.56 \mathrm{cm}, \mathrm{PE}=0.18 \mathrm{cm}, \mathrm{PF}=0.36 \mathrm{cm}$, find out whether $\mathrm{EF}\parallel \mathrm{QR}$.

In the figure given below, $\mathrm{CD}\parallel \mathrm{LA}$ and $\mathrm{DE}\parallel \mathrm{AC}$. Find the length of $\mathrm{CL}$ if $\mathrm{BE}=4 \mathrm{cm}$ and $\mathrm{EC}=2 \mathrm{cm}$.

In the figure given below, $\angle D=\angle E$ and $\frac{AD}{DB}=\frac{AE}{EC}$. Prove that $ABC$ is an isosceles triangle.

In the figure given below, the points  $\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ are located respectively on $\mathrm{OP}, \mathrm{OQ}$ and $\mathrm{OR}$ in such way that $\mathrm{AB}\parallel \mathrm{PQ}$ and $\mathrm{AC}\parallel \mathrm{PR}$. Show that $\mathrm{BC}\parallel \mathrm{QR}$.

$ABCD$ is a trapezium in which $AB\parallel DC$ and its diagonals intersect each other at point $\text{'}O\text{'}.$ Show that $\frac{AO}{BO}=\frac{CO}{DO}$.