Jitender Gupta and Divya Malik Solutions for Exercise 1: Topic Exercise

In the given figure, if $\angle \mathrm{A}=\angle \mathrm{C}, \mathrm{AB}=6 \mathrm{cm}, \mathrm{BP}=15 \mathrm{cm}, \mathrm{AP}=12 \mathrm{cm}$ and $\mathrm{CP}=4 \mathrm{cm}$ and the lengths of $\mathrm{PD}+\mathrm{CD}=k \mathrm{cm}$, then find the value of $k$.

In the given figure, $\angle \mathrm{M}=\angle \mathrm{N}=46°$ and $x, a, b$ and $c$ are the lengths of $\mathrm{PN}, \mathrm{LM}, \mathrm{MN}$ and $\mathrm{NK}$, respectively, if $x$ in terms of $a, b, c$ is $\frac{k}{b+c}$ then find $k$

A $15 \mathrm{m}$ high tower casts a shadow $24 \mathrm{m}$ long at a certain time and at the same time, telephone pole casts a shadow $16 \mathrm{m}$ long. Find the height of the telephone pole.

$△{\mathrm{ABC}}_{}$and $△\mathrm{AMP}$ are two right-angled triangles, right-angled at $\mathrm{B}$ and $\mathrm{M}$, respectively. Prove that $\mathrm{CA}\times \mathrm{MP}=\mathrm{PA}\times \mathrm{BC}.$

In a $△\mathrm{ABC}, \mathrm{P}$ and $\mathrm{Q}$ are points in $\mathrm{AB}$ and $\mathrm{AC}$, respectively and $\mathrm{PQ}\parallel \mathrm{BC}$. Prove that the median bisects $\mathrm{PQ}$.

In the given figure, find the value of $\mathrm{x}$, if $\mathrm{DE}\parallel \mathrm{BC}$. Write the answer in centimeter.

In $△\mathrm{ABC}$, $\mathrm{P} \mathrm{and} \mathrm{Q}$ are points on $\mathrm{AB}$ and $\mathrm{AC}$ such that $\mathrm{PQ}\parallel \mathrm{BC}$. If $\mathrm{AP}=4 \mathrm{cm}, \mathrm{AQ}=3 \mathrm{cm}$ and $\mathrm{PB}= 2 \mathrm{cm}$, then find the value of $\mathrm{AC}$. Write the answer in centimeters.

In the given figure, if $\frac{AD}{DC}=\frac{BE}{EC}$ and $\angle CDE=\angle CED$, then prove that $△CAB$ is isosceles triangle.