Construction of a Quadrilateral in Different Situations

Q.

The sum of the length of any two sides of a triangle is always equal to the third side.

True

False

Q.

A triangle with sides 2cm, 3cm and 5cm is possible.

1. True

2. False

Q.

How many degrees are there in three right angles?

Q.

The hypotenuse of a right angled triangle is 5cm and the other two sides differ by 1cm . Find the lengths of the sides of the triangle

Q. If the measure of 3 sides of a quadrilateral is given, which among the following measurements are required to construct a unique quadrilateral?

1. 2 diagonals
2. 1 side
3. 1 diagonal
4. 1 angle

Q.

The sides of a triangle are in the ratio 5:7:8. If the perimetre of the triangle is 100 cm, find the lenght of the sides of the triangle.

Q.

How many degrees are there in five right angles?

Q.

Can the sides of a triangle be in the ratio 1 : 2 : 3?

Q. The sum of all the angles of a triangle is

1. ${360}^{\circ }$
2. ${90}^{\circ }$
3. ${180}^{\circ }$
4. ${150}^{\circ }$

Q. ___ is a quadrilateral which has exactly one pair of opposite angles that are equal.

1. Parallelogram
2. Kite
3. Rhombus
4. Square

Q.

In a triangle sum of lengths of any two sides must be less than the third side.

1. True

2. False

Q.

How many degrees are there in one right angle.

Q. The sum of all the angles of a triangle is

1. ${360}^{\circ }$
2. ${90}^{\circ }$
3. ${180}^{\circ }$
4. ${150}^{\circ }$

Q. A quadrilateral can be constructed by constructing 2 triangles having a common side. True/False.

1. False
2. True

Q.

Prove that for any quadrilateral with a pair of opposite sides parallel, the area is half the product of the sum of the lengths of the parallel sides and the distance between them.

Q.

There is a quadrilateral PLAY with PL = 3cm, LA = 4cm, AY = 4.5 cm, PY = 2cm. Which of the following values of LY is not possible?

1. 2

2. 3

3. 6

4. 4

Q.

The sum of the measures of three angles of a triangle is greater than $180°$. State whether the statement is True or False.

1. True
2. False

Q.

Can we draw a quadrilateral ABCD with following measurements: AB = 3cm, BC = 5cm, AD = 4cm, CD= 7cm and BD=8cm?

1. No, it is impossible

2. With the measure of extra angle, Yes

3. With the measure of other diagonal, Yes

4. Yes, definitely

Q. If the measure of sides of a quadrilateral are given as AB = 7cm, AD = 5 cm and BD = 10 cm. Can you draw a quadrilateral ABCD?

1. Yes
2. No
3. Yes, if BC is given.
4. Yes, if BC and CD is given.

Q.

A triangle with sides 2 cm, 3 cm and 5 cm is possible. (True/False)

1. True

2. False

Q.

A triangle has 2 sides, 5 cm and 6 cm respectively. What value must the 3rd side be greater than (in cm)?

___

Q.

What is the name of a twelve-sided polygon?

1. dodecagon

2. decagon

3. nonagon

4. octagon

Q.

Let ABC be a triangle and P be an interior point. Prove that AB + BC + CA < 2(PA + PB + PC).

Q.

A triangle has two sides given as 5 cm and 6 cm. The third side must be smaller than what (in cm)?

___

Q.

If the measure of the sides of a quadrilateral are given as AB = 4cm, CD = 5cm, and angles are given as ∠ ABC = ${75}^{\circ }$, ∠ BCD = ${35}^{\circ }$ and ∠ CDA = ${135}^{\circ }$, can you construct a quadrilateral ABCD?

1. Yes

2. No

3. With the measure of $\angle$ DAB, Yes

4. With the measure of BC, Yes

Q.

For a quadrilateral PQRS where PQ = 4 cm, QR = 6 cm, RS = 5 cm, PS = 5.5 cm. The length of PR should be less than

__

Q.

Tick the correct answer:

The sum of all interior angles of a triangle is :

1. $0$

2. $360°$

3. $180°$

4. $270°$

Q. ___ is a quadrilateral which has exactly one pair of opposite angles that are equal.

1. rhombus
2. parallelogram
3. kite
4. square

Q.

How many quadrilaterals can I construct with the following data: Quadrilateral PQRS with PQ = 4.5 cm, Angle P = ${70}^{\circ }$, Angle Q = ${100}^{\circ }$, Angle R = ${80}^{\circ }$ and Angle S =${110}^{\circ }$.

1. 0

2. 1

3. 2

4. Infinite

Q.

Construct a quadrilateral ABCD given AB = 5.6 cm, BC = 4.1, CD = 4.4 cm, AD = 3.3 cm and $\angle A={75}^{\circ }$ [3 MARKS]