Construction of Quadrilateral (3 Sides and 2 Diagonals)

Q.

Construct the following quadrilateral: Quadrilateral $\text{TRUE. TR = 3.5 cm, RU = 3 cm, UE = 4 cm, ∠R = 75°, ∠U = 120°}$

Q.

It is possible to construct a unique quadrilateral ABCD with AB = 5cm, BC = 6cm, CD = 7cm , $\angle ABC$ = ${45}^{\circ }$ and $\angle BCD$ = ${55}^{\circ }$.

1. No, two such quadrilaterals can be constructed

2. Yes, it is possible

Q. Construct a rhombus ABCD, with diagonals AC = 6 cm and BD = 4.6 cm.

Q.

We know the lengths of two adjacent sides and three angles in a quadrilateral. In how many ways can the construction be started?

__

Q.

If there is a quadrilateral ABCD and you have measures of any three sides and two diagonals of the quadrilateral ABCD, can you construct it?

1. No, it is impossible.

2. Yes, definitely.

3. With a measure of one angle too, yes.

4. I can construct half quadrilateral.

Q.

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

1. No, it is impossible

2. With the measure of extra angle, Yes

3. With the measure of another diagonal, Yes

4. Yes definitely

Q.

In quadrilateral PQRS, PQ=4cm, QR= 3cm, RS= 5.9cm, QS =4.8cm and PR=5.5cm. Find the value of PS using constructions.

1. 1 cm

2. 2 cm

3. 4 cm

4. 3 cm

Q.

Which one of the given statements is correct

1. Statement 3

2. Statement 2

3. Statement 1

4. Statement 4

Q.

We can construct an unique quadrilateral ABCD with AB = 4 cm, BC = 6 cm, AC = 7 cm, CD = 5 cm and BD = 8 cm.

1. True

2. False

Q. Construct a quadrilateral PQRS in which PQ = 6 cm, QR = 5.6 cm, RS = 2.7 cm, ∠Q = 45° and ∠R = 90°.

Q.

What is the last step in constructing quadrilateral with 3 sides and 2 included angles given?

1. Draw line segment

2. Draw arc

3. none of these

4. Construct triangle

Q. Construct a cyclic quardilateral $ABCD$ in which vertical angle $\angle B={65}^o,AB=4cm,AC=6cm$ and $AD=4cm$. Write the steps of construction also.

Q. In the figure given below, all the four sides are equal. The construction of which figure is shown in the diagram?

1. Kite
2. Rhombus
3. Rectangle
4. Trapezium

Q.

In a quadrilateral PQRS, PQ = 4 cm, QR = 3 cm, RS = 5.9 cm, QS = 4.8 cm and PR = 5.5 cm. Find the value of PS.

1. 3 cm

2. 4 cm

3. 1 cm

4. 2 cm

Q.

To construct a rhombus given the measure of its two diagonals, which property of the rhombus do we use?

1. 1

2. 2

3. 4

4. 3

Q. We know that, a quadrilateral is constructed when its minimum 5 measurments are given. Name any two methods of construction. [2 MARKS]

Q.

In quadrilateral PQRS, PQ = 4 cm, QR = 3 cm, RS = 5.9 cm, QS = 4.8 cm and PR = 5.5 cm. Find the value of PS using constructions.

1. 1cm

2. 3cm

3. 2cm

4. 4cm

Q. Construct a quadrilateral $ABCD$ in which $AB=BC=3.0cm,AD=CD=5.0cm$ and $\angle ABC={120}^o$.

Q.

To construct a parallelogram given its length of diagonals, which of the following additional information is required?

1. One angle of the parallelogram

2. Two angles of the parallelogram

3. The angle between the diagonals

4. None of the above

Q. Find the value of $x$ in each figure.

1. ${65}^{\circ }$
2. ${70}^{\circ }$
3. ${105}^{\circ }$

Q.

If there is a quadrilateral ABCD and you have measures of any three sides and two diagonals of the quadrilateral ABCD, can you construct it?

1. Yes, definitely

2. With a measure of one angle too, yes

3. I can construct half quadrilateral

4. No, it is impossible

Q. All squares are rectangles.

1. False
2. True

Q. Given below are the steps of construction of a quadrilateral ABCD, where AB = 3.5 cm, BC = 6.5 cm, $\angle A={75}^{\circ },\angle B={105}^{\circ }$ and $\angle C={120}^{\circ }$. Which of the following options is the wrong step?
1:- Draw AB = 3.5 cm.
2:- Draw $\angle DAB={75}^{\circ },\angle ABC={105}^{\circ }$ at B.
3:- Draw BC = 6.5 cm.
4:- At D draw $\angle ADC={120}^{\circ }$.

1. 4
2. 2
3. 3
4. 1

Q.

To construct a rhombus given the measure of its two diagonals, which property of the rhombus do we use?

1. Diagonals bisect each other at ${90}^{\circ }$

2. Opposite angles are equal.

3. Diagonals bisect each other

4. All sides are equal

Q. Sort steps to construct quadrilateral ABCD with AB, BC, CD, AD, AC as 4 cm, 6 cm, 5.5 cm, 5 cm, 8 cm.

1. $WithAascentre,\mathrm{draw}\mathrm{an}\mathrm{arc}ofradius5cm\mathrm{to}\mathrm{the}\mathrm{opposite}\mathrm{side}\mathrm{of}\mathrm{AC}.$
2. $\mathrm{With}Cascentre,drawanarcofradius6cmandmarkthe\mathrm{point}\mathrm{of}\mathrm{intersection}withthearcdrawninstep2asB.\mathrm{Join}\mathrm{AB}\mathrm{and}\mathrm{CB}.$
3. $\mathrm{With}Aascentre,\mathrm{draw}\mathrm{an}\mathrm{arc}ofradius4cm.$
4. $\mathrm{Draw}a\mathrm{line}\mathrm{segment}\mathrm{AC}\mathrm{of}8\mathrm{cm}.$
5. $WithCascentre,drawanarcofradius5.5\mathrm{cm}andmarkthepointofintersectionwiththearc\mathrm{drawn}\mathrm{in}\mathrm{step}4asD.\mathrm{Join}\mathrm{AD}\mathrm{and}\mathrm{CD}.$

Q. Construct a quadrilateral PQRS, in which PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1 cm, ∠Q = 75° and ∠R = 120°.

Q. Given below are the steps of construction of a quadrilateral ABCD, where AB = 3.5 cm, BC = 6.5 cm, $\angle A={75}^{\circ },\angle B={105}^{\circ }$ and $\angle C={120}^{\circ }$. Which of the following options is the wrong step?
1:- Draw AB = 3.5 cm.
2:- Draw $\angle DAB={75}^{\circ },\angle ABC={105}^{\circ }$ at B.
3:- Draw BC = 6.5 cm.
4:- At D draw $\angle ADC={120}^{\circ }$.

1. 2
2. 1
3. 3
4. 4

Q.

To construct a rhombus given the measure of its two diagonals, which property of the rhombus do we use?

1. Diagonals bisect each other

2. Diagonals bisect each other at ${90}^{\circ }$

3. Opposite angles are equal.

4. All sides are equal

Q. Given below are the steps of construction of a quadrilateral ABCD, where AB = 3.5 cm, BC = 6.5 cm, $\angle A={75}^{\circ },\angle B={105}^{\circ }$ and $\angle C={120}^{\circ }$. Which of the following options is the wrong step?
1:- Draw AB = 3.5 cm.
2:- Draw $\angle DAB={75}^{\circ },\angle ABC={105}^{\circ }$ at B.
3:- Draw BC = 6.5 cm.
4:- At D draw $\angle ADC={120}^{\circ }$.

1. 1
2. 2
3. 4
4. 3