Exercise

In the given figure, $\angle PQR=\angle PST=90°, PQ=5 \mathrm{cm}$ and $PS = 2 \mathrm{cm}$. Find Area of $△PQR :$ Area of quadrilateral $SRQT$.

In figure, $O$ is any point in the interior of $∆ABC$. If $OD\perp BC,OE\perp AC$ and $OF\perp AB$, show that

$O{A}^2+O{B}^2+O{C}^2-O{D}^2-O{E}^2-O{F}^2=A{F}^2+B{D}^2+C{E}^2$.

A ladder $15 \mathrm{m}$ long reaches a window which is $9 \mathrm{m}$ above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to other side of the street to reach a window $12 \mathrm{m}$. Find the width of the street.

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

In the given figure, $\angle PQR = \angle PST = 90°, PQ = 5 \mathrm{cm}$ and $PS = 2 \mathrm{cm}$. Prove that $△PQR ~ △PST$.

Is the pair of polygons given below similar or not similar? Why? 

In $△ACB, \angle C=90°$ and $CD\perp AB$. Prove that $\frac{B{C}^2}{A{C}^2}=\frac{BD}{AD}$.

Check for similarity in the triangles and explain which criterion is used.

$\text{△OAB}$ and $\text{△OKT}$