Properties of Quadrilaterals

Q. A square whose side is 2m has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon in meters is

Q. Name the regular polygon whose each exterior angle measures ${72}^{\circ }$.

1. Heptagon
2. Pentagon
3. Septagon
4. Octagon

Q.

Square has all the properties of

1. Rectangle and kite

2. Rhombus and kite

3. Parallelogram, kite and rhombus

4. Rectangle, rhombus and parallelogram

Q.

Given the three side lengths, how can you tell if a triangle is a right triangle?

Q. Question 11
Is it possible to construct a triangle with lengths of its sides as 9 cm, 7 cm and 17 cm? Give reason for your answer.

Q. In the adjacent figure, the bisectors of $\angle A$ and $\angle B$ meet at a point P. If $\angle C={100}^0$ and $\angle D={60}^0$, find the measure of $\angle APB$.

1. ${80}^{\circ }$
2. ${90}^{\circ }$
3. ${120}^{\circ }$
4. ${100}^{\circ }$

Q. Quadrilateral LAMP with AM = MP = PL = 5cm, $\angle M={90}^{\circ }$ and $\angle P={60}^{\circ }$

Q. If i join two right angle triangles. will it be a quadrilateral ?

Q.

In a rhombus, if the measure of one angle is 60 degrees then the measure of its adjacent angle is:

1. 90^o

2. 60^o

3. 150^o

4. 120^o

Q.

Find the measure of each exterior angle of a regular polygon of $9$ sides.

Q. Jhon is constructing a parallelogram ABCD, in which diagonal AC = 3.8 cm, diagonal BD = 4.6 cm and the angle between AC and BD is 60°. Can he complete the construction using the above given measurements?

1. One more angle should be given.
2. Yes, only if the length of one side is given.
3. No
4. Yes

Q.

Construct a triangle PQR in which PQ + PR = 6.5 cm, QR = 5.4 cm and ∠Q = 40°.

Q. Identify the type of polygon represented in the figure given below.

1. 1 is concave, 2 is convex
2. 1 is convex, 2 is concave
3. Both are concave and convex quadrilaterals
4. They are neither concave nor convex.

Q. If PQRS is a rhombus and angle P = 70 degrees, then what is the value of angle PQR?

1. 35 degrees
2. 55 degrees
3. 45 degrees
4. 110 degrees

Q. The angles of a quadrilateral are x°, (x-10)°, (x+ 30)° and 2x°. Then find the value of the greatest angle.

1. ${136}^0$
2. ${180}^0$
3. ${98}^0$
4. ${68}^0$

Q.

Diagonals of a rectangle are

1. Equal

2. Bisect each other

3. Perpendicular bisector of each other.

4. Not equal

Q. For the construction of a rhombus, we just require the measure of one side and one diagonal. State whether the statement is true or false.

1. True
   
2. 
   False
   
   

Q.

Construct a triangle ABC whose perimeter is 9 cm and the angles are in the ratio 3:4:5.

Q.

Construct a right angle triangle ABC in which ∠B = 90°, BC = 4 cm and AC = 5 cm.

Q. The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the measure of each of these angles.

1. ${55}^{\circ },{95}^{\circ },{95}^{\circ },{115}^{\circ }$
2. ${35}^{\circ },{115}^{\circ },{75}^{\circ },{135}^{\circ }$
3. ${85}^{\circ },{85}^{\circ },{65}^{\circ },{125}^{\circ }$
4. ${45}^{\circ },{75}^{\circ },{105}^{\circ },{135}^{\circ }$

Q.

A rope is tied to the opposite corners of a square field of side 122 m .find the length of the Rope correct to two decimal places.

Q. construct a triangle ABC in which BC = 6.5 cm, angle B =60* and angle c = 70*.

Q.

Construct a triangle ABC in which BC = 5.2 cm, ∠B = 35° and ∠C = 80°.

Q. Measurements of which of the following parts would be sufficient to construct a quadrilateral?

1. 3 angles and their 2 included sides
2. 3 sides only
3. 2 diagonals only
4. 5 sides and 3 diagonals

Q. In a rhombus PQRS, the angle P is three times angle Q. Find angle P.

1. 30 degrees
2. 45 degrees
3. 60 degrees
4. 135 degrees

Q. In a square ABCD, if BC = (3x + 4) cm and CD = (5x - 2) cm, the length of AB is:

1. 12 cm
2. 13 cm
3. 10 cm
4. 11 cm

Q.

Construct a triangle ABC whose perimeter is 12 cm and the angles are in the ratio 2:3:5.

Q. Which of the following quadrilaterals have their opposite sides equal?

1. Kite
2. Trapezium
3. Rhombus
4. Any quadrilateral

Q.

Five equal rhombus of side 2 cm are arranged in the following manner:

What additional information do you require to draw this figure?

1. $\angle$ IFG = 60${}^{\circ }$

2. $\angle$ IHG = 60${}^{\circ }$

3. $\angle$ IFG = 45${}^{\circ }$

4. HG = FG = 2cm, FE = ED = 1 cm

Q.

A square is a _______ with equal sides.

1. Trapezium

2. Rectangle

3. Rhombus

4. Kite