Polygons

Q.

$△$ABC is a right angled triangle, right angled at B. BD is a perpendicular as shown. Prove that:

${AB}^2$ = ${AD}^2$ + ${BC}^2$ - ${CD}^2$

Q. ΔPQR is a triangle right-angled at P. If PQ = 3 cm and PR = 4 cm, find QR.

1. 3 cm
2. 7 cm
3. 5 cm
4. 8 cm

Q. ABC is an isosceles triangle with AB = BC. Find the ∠A.

1. 60°
2. 70°
3. 80°
4. 75°

Q.

A regular polygon of 8 sides is called an _____.

Q.

What is a six-sided polygon called?

1. Hexagon

2. Heptagon

3. Pentagon

4. Octagon

Q. In an isosceles $△ABC,AB=AC$ and $\angle BAC={30}^{\circ }$. Find the remaining angles.

1. $\angle ABC={30}^{\circ }$ and $\angle ACB={120}^{\circ }$
2. $\angle ABC={60}^{\circ }$ and $\angle ACB={90}^{\circ }$
3. $\angle ABC=\angle ACB={60}^{\circ }$
4. $\angle ABC=\angle ACB={75}^{\circ }$

Q. Match the polygons with their respective number of sides.

1. 8
2. 10
3. 12

Q. ΔPQR is a triangle right-angled at P. If PQ = 3 cm and PR = 4 cm, find QR.

1. 3 cm
2. 7 cm
3. 5 cm
4. 8 cm

Q. In an isosceles $△ABC,AB=AC$ and $\angle BAC={30}^{\circ }$. Find the remaining angles.

1. $\angle ABC={30}^{\circ }$ and $\angle ACB={120}^{\circ }$
2. $\angle ABC={60}^{\circ }$ and $\angle ACB={90}^{\circ }$
3. $\angle ABC=\angle ACB={60}^{\circ }$
4. $\angle ABC=\angle ACB={75}^{\circ }$

Q. Draw a rough sketch of a regular octagon. (Use squared paper if you wish). Draw a rectangle by joining exactly four of the vertices of the octagon.

Q.

A polygon having $\_\_\_\_\_\_\_\_\_\_\_\_\_$ sides is called octagon.

Q.

In the given isosceles triangle ABC, AB = AC, $\angle ABC$ = 70°. Find $\angle$ BAC.

1. ${60}^{\circ }$

2. ${50}^{\circ }$

3. ${40}^{\circ }$

4. ${45}^{\circ }$

Q. Which among the following quadrilaterals are regular polygons?​

Q. A polygon has prime number of sides. If number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is

1. $10$
2. $4$
3. $5$
4. $7$

Q. Each equal part of the circle is called

1. semicircle
2. major circle
3. minor circle
4. none

Q. In an isosceles $△ABC,AB=AC$ and $\angle BAC={30}^{\circ }$. Find the remaining angles.

1. $\angle ABC={30}^{\circ }$ and $\angle ACB={120}^{\circ }$
2. $\angle ABC={60}^{\circ }$ and $\angle ACB={90}^{\circ }$
3. $\angle ABC=\angle ACB={60}^{\circ }$
4. $\angle ABC=\angle ACB={75}^{\circ }$

Q. In an isosceles $△ABC,AB=AC$ and $\angle BAC={30}^{\circ }$. Find the remaining angles.

1. $\angle ABC={30}^{\circ }$ and $\angle ACB={120}^{\circ }$
2. $\angle ABC={60}^{\circ }$ and $\angle ACB={90}^{\circ }$
3. $\angle ABC=\angle ACB={60}^{\circ }$
4. $\angle ABC=\angle ACB={75}^{\circ }$

Q.

The number of sides of an octagon is_______________