Construction of Quadrilateral Given 3 Sides and 2 Included Angles

Q. Question 75

___ measurements can determine a quadrilateral uniquely.

Q.

It is possible to construct a quadrilateral ABCD in which AB=5cm, BC=7.5cm, $\angle A={80}^{\circ },\angle B={140}^{\circ },\angle C={145}^{\circ }$?

Q.

In which of the following cases, a unique and stable quadrilateral cannot be constructed?

1. When all 4 sides of a quadrilateral are given

2. When three sides and one base angle is given.

3. When two angles and three sides are given

4. Constructing a rhombus when lengths of its diagonals are given.

Q.

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

1. Draw arc

2. Construct triangle

3. none of these

4. Draw line segment

Q. To construct a quadrilateral, we need to know three sides and _____ included angles.

1. four
2. one
3. three
4. two

Q.

We cannot construct a quadrilateral PQRS with PQ =6cm, QR = 5 cm, ∠P = 70^o, ∠Q = 150^o and the measurement of ∠R as

1. 70^o

2. 100^o

3. 80^o

4. 140^o

Q.

Is it possible to construct a unique quadrilateral ABCD with AB = 5cm, BC = 6cm, CD= 7cm, $\angle$ABC = ${40}^{\circ }$ and $\angle$ BCD = ${55}^{\circ }$?

1. Yes, it is possible

2. No, two such quadrilaterals can be constructed

3. No, there can be infinite such quadrilaterals

4. With the measure of an extra side, yes.

Q.

Construct a quadrilateral XYZW in which XY = 5 cm, YZ = 6 cm, ZW = 7 cm, WX = 3 cm and XZ = 9 cm.

Q. Which of the following unique quadrilaterals can be constructed if the measure of only two adjacent sides are given?

1. Rhombus
2. Rectangle
3. Parallelogram
4. All of the above

Q.

In the construction of quadrilateral PQRS, with PQ = 3 cm, QR = 4 cm and PS = 5 cm, also, $\angle$SPQ = ${70}^{\circ }$ and $\angle$PQR = ${90}^{\circ }$, which of the sides is to be taken as base and constructed first?

1. PQ

2. QR

3. RS

4. PR

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. Construct triangle

4. None of these

Q. To construct a quadrilateral, we need to know three sides and _____ included angles.

1. two
2. three
3. four
4. one

Q. Question 125
State whether the statements are True or False.
A quadrilateral can be drawn, when all the four angles and one side is given.

Q. Which of the following unique quadrilaterals can be constructed if the measure of only two adjacent sides are given?

1. Rectangle
2. Parallelogram
3. Rhombus
4. All of the above

Q.

In the construction of quadrilateral PQRS, with PQ = 3 cm, QR = 4 cm and PS = 5 cm, also, $\angle$SPQ = ${70}^{\circ }$ and $\angle$PQR = ${90}^{\circ }$, which of the sides is to be taken as base and constructed first?

1. PQ

2. QR

3. RS

4. PR

Q.

State true or false.

I can construct a quadrilateral with 3 sides and 2 included angles measuring ${75}^{\circ }$ and ${105}^{\circ }$. The quadrilateral is a trapezium.

1. False

2. True

Q.

Construction of a unique quadrilateral is possible if we have a minimum measurement of 3 sides and ____ included angles.

1. 4

2. 1

3. 2

4. 3

Q. Can you draw a unique triangle with any 3 possible measurements of sides or angles?

1. Yes
2. With 3 angles, Yes; With 3 sides, No
3. With 3 sides, Yes; With 3 angles, No.
4. No, not possible.

Q.

Construction of a unique quadrilateral is possible if we have a minimum measurement of 3 sides and ___included angles.

Q.

In a quadrilateral PQRS, PQ = 3 cm, QR = 4 cm and PS = 5 cm. Also, $\angle$SPQ = ${70}^{\circ }$ and $\angle$PQR = ${90}^{\circ }$. Which of the following options is the approximate value of $\angle$QRS?

1. 

2. 

3. 

4. 

Q.

In the construction of quadrilateral PQRS, with PQ = 3 cm, QR = 4 cm and PS = 5 cm, also, $\angle$SPQ = ${70}^{\circ }$ and $\angle$PQR = ${90}^{\circ }$, which of the sides is to be taken as base and constructed first?

1. PQ

2. PR

3. RS

4. QR

Q.

Construction of a unique quadrilateral is possible if we have a minimum measurement of 3 sides and ____ included angles.

1. 2

2. 3

3. 4

4. 1

Q. If you are given AB = 5 cm, BC = 6 cm, CD = 7 cm, DA = 6 cm and $\angle ABC={60}^{\circ }$, can you draw a quadrilateral?
$\left[3Marks\right]$

Q. To construct a quadrilateral, we need to know three sides and _____ included angles.

1. two
2. three
3. four
4. one

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. Construct triangle

4. None of these

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. Construct triangle

4. None of these

Q. 4 sides and the measure of any angle is sufficient to construct a unique quadrilateral.

1. True
2. False

Q. In a quadrilateral PQRS, PQ = 3 cm, QR = 4 cm and PS = 5 cm. Also, $\angle SPQ$ = ${70}^{\circ }$ and $\angle PQR$ = ${90}^{\circ }$. Which of the following options is the approximate value of $\angle QRS$?

1. ${100}^{\circ }$
2. ${90}^{\circ }$
3. ${110}^{\circ }$
4. ${118}^{\circ }$

Q. In □PLAY, l(PL) = 4.5 cm, l(LA) = 6.5 cm, l(PY) = 5.5 cm, l(PA) = 8.5 cm, l(LY) = 7.5 cm