Similar Figures

A model of a square $PQRS$ is made to a scale of $0.006$. The area of the square on the model is $150 {\mathrm{cm}}^2$. If the actual area of the square is $k {\mathrm{cm}}^2$, then find the value of $k$.

A model of a ship is made to a scale of $1:200$. The volume of the model is $100 \mathrm{L}$. If the volume of the ship is $x \mathrm{L}$, then find the value of $x$. 

$AD$ is a diameter of the circumcircle of $△ABC$. $AE$ is perpendicular to $BC$. Prove that $AB.AC=AD.AE$

A model of a square $PQRS$ is made to a scale of $0.006$. The area of the square on the model is $150 {\mathrm{cm}}^2$. If the actual area of the square is $k {\mathrm{cm}}^2$, then find the value of $k$.

A model of a ship is made to a scale of $1:200$. The volume of the model is $100 \mathrm{L}$. If the volume of the ship is $x \mathrm{L}$, then find the value of $x$. 

If $\Delta ABC$ is right angled at $B$, where $A(5,6,4), B(4,4,1)$ and $C(8,2,x)$ then find the value of $x$ is

All the equilateral triangles are _____.

In the given figure, $∆\mathrm{ABC}~∆\mathrm{QPR}$. Then $\angle \mathrm{R}$ is:

The polygons having the same number of sides are similar if 

(a)__________ .              (b)_____________.

$\mathrm{ABC}$ is a right triangle with angle $\mathrm{B}=90°.$ A circle with $\mathrm{BC}$ as diameter meets hypotenuse $\mathrm{AC}$ at point $\mathrm{D}.$ Prove that $\mathrm{AC} \mathrm{X} \mathrm{AD}={\mathrm{AB}}^2$.
 

$\mathrm{ABC}$ is a right triangle with angle $\mathrm{B}=90°$. A circle with $\mathrm{BC}$ as diameter meets hypotenuse $\mathrm{AC}$ at point $\mathrm{D}$. Prove that ${\mathrm{BD}}^2=\mathrm{AD}\times \mathrm{DC}$.

All equiangular triangles are similar.

Two congruent polygons are necessarily similar.

Two similar polygons are necessarily congruent.

All the equilateral triangles are _____. (similar, congruent)

The polygons having the same number of sides are similar, if 

• corresponding angles are equal,
• corresponding sides are _____. 

All circles are _____. (Similar/Different)

 All the squares are _____.

Two polygons having corresponding angles equal are similar.

Give any two examples of similar figures with their diagrams.