M L Aggarwal Solutions for Exercise 1: Exercise 13.1

Calculate the other sides of a triangle whose shortest side is $6 \mathrm{cm}$ and which is similar to a triangle whose sides are $4 \mathrm{cm}, 7 \mathrm{cm}$ and $8 \mathrm{cm}$.

In the figure given below, $AB\parallel DE, AC=3 \mathrm{cm}, CE=7.5 \mathrm{cm}$ and $BD=14 \mathrm{cm}$. Calculate $CB$ and $DC$.

In the figure given below, $CA\parallel BD$, the lines $AB$ and $CD$ meet at $O$. Prove that $△ACO~△BDO$.

In the figure given below, $CA\parallel BD$, the lines $AB$ and $CD$ meet at $O$. If $BD=2.4 \mathrm{cm}, OD=4 \mathrm{cm}, OB=3.2 \mathrm{cm}$ and $AC=3.6 \mathrm{cm}$, calculate $OA$ and $OC$.

In the figure given below, $AP=2PB$ and $CP=2PD$. If $AC=4.5 \mathrm{cm}$, calculate the length of $BD$.

In the figure given below, $\angle ADE=\angle ACB$. Prove that $△ABC$ and $△AED$ are similar.

In the figure given below, $\angle PQR=\angle PRS$. Prove that triangles $PQR$ and $PRS$ are similar. If $PR=8 \mathrm{cm}, PS=4 \mathrm{cm}$, calculate $PQ$.

In the figure given below, $AF, BE$ and $CD$ are parallel lines. Given that $AB=15 \mathrm{cm}, EG=5 \mathrm{cm}, GC=10 \mathrm{cm}$ and $DC=18 \mathrm{cm}$. Calculate $AC$.