Similar Figures

In the given figure, the value of $x$ is

Saloni constructed a triangle ABC with angle measures as $45°, 50°, \mathrm{and} 85°$. Sunita constructed another triangle $\mathrm{PQR}$ with the same angle measures. Is it necessary that the side lengths of triangles $\mathrm{ABC}$and $\mathrm{PQR}$ would also be the same$?$ Justify your answer.

If two geometrical figures are similar, their corresponding sides are:

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

All the equilateral triangles are _____.

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.

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.

Two polygons are similar if their corresponding sides are proportional and corresponding angles are equal.

Two polygons having same ratio of their corresponding sides are similar.

Two similar figures are congurent.

Two congruent figures are similar.