Quadrilaterals

Q. There are ___ vertices of a triangle.

Q.

Prove that each angle of a rectangle is ${90}^{\circ }$.

Q.

What is the measure of each exterior angle of a regular $30$ sided polygon?

Q. Question 13
Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

Q. In the diagram, ABCD is a rhombus. AEC and BED are straight lines. Find the value of $p+q+r+s+t$

1. ${200}^{\circ }$
2. ${270}^{\circ }$
3. ${360}^{\circ }$
4. ${540}^{\circ }$

Q.

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Q.

$△ABC$ is a right-angled triangle and $O$ is the mid-point of the side opposite to the right angle. Explain why $O$is equidistant from $A,B$ and $C.$

Q.

If two parallel lines are intersected by a transversal then the bisectors of the interior angles form a :

1. Square

2. Rectangle

3. parallelogram

4. rhombus

Q. ABCD is parallelogram. The angle bisectors of ∠A and ∠D intersect at O. Find the measures of ∠AOD.

Q.

Find the angle sum of all interior angles of a regular polygon which has 7 sides.

1. 180 ^o

2. 540 ^o

3. 900 ^o

4. 960 ^o

Q.

__ is defined as the line segment joining the opposite vertices of a quadrilateral.

Q. Find the value of x in the following quadrilateral.

1. 85°
2. 95°
3. 90°
4. 185°

Q.

The opposite sides of a quadrilateral have

1. infinitely many common points

2. no common point

3. one common point

4. two common points

Q.

The interior angle of a regular polygon is double the exterior angle. The number of sides of the polygon is

1. 10

2. 6

3. 12

4. 8

Q.

The consecutive sides of a quadrilateral have

Q.

Can all the four angles of a quadrilateral be obtuse angles? Give a reason for your answer.

Q. Using opposite angles test for parallelogram, prove that every rectangle is a parallelogram.

Q.

Each interior angle of a regular polygon is 144°. The measure of each interior angle of a regular polygon which has double the number of sides as the first polygon is

1. ${150}^{\circ }$

2. ${152}^{\circ }$

3. ${160}^{\circ }$

4. ${162}^{\circ }$

Q. Prove that quadrilateral formed by the intersection of angle bisectors of all angles of a parallelogram is a rectangle.(shown in the given figure)

Q.

The point which lie on the same line are called ________

Q.

In a quadrilateral ABCD AB = 6 cm, BC = 8 cm, CD = 8 cm and AC=10cm.The area of the quadrilateral is 60.67 cm². Find DA.
[4 MARKS]

Q.

Draw a hexagon with all sides equal, but not all angles equal.

Q.

Find the measure of each interior and exterior angle of a regular $40-\mathrm{gon}$.

Q. Prove that the sum of all the angle of a quadrilateral is ${360}^{\circ }.$

Q.

The numbers of sides of two regular sides of two regular polygons are in the ratio 4: 5 and their interior angles are in the ratio 15: 16, find the difference in the number of sides of the polygons.

1. 2

2. 3

3. 1

4. 4

Q.

Which of the following is not a quadrilateral?

1. Square

2. Circle

3. Rhombus

4. Trapezium

Q. Which of the following quadrilateral is not a rhombus?

(a) All four sides are equal

(b) Diagonals bisect each other

(c) Diagonals bisect opposite angles

(d) One angle between the diagonals is 60°

Q. In the figure given below, if $\angle AOP={75}^{\circ }$ and $\angle AOB={120}^{\circ }$, then $\angle AQP$= ___.

1. ${55}^{\circ }$
2. ${37.5}^{\circ }$
3. ${30}^{\circ }$
4. ${22.5}^{\circ }$

Q. ABCD is a quadrilateral ; P, Q, R and S are the points of trisection of side AB , BC , CD and DA respectively and are adjacent to A and C; prove that PQRS is a paralle\log ram.

Q. Circumcentre of a right-angled triangle lies outside the triangle.

1. True
2. False