Construction of a Quadrilateral When Two Adjacent Sides and Three Angles Are Given.

Q.

Construct a quadrilateral PQRS in which PQ = 5 cm, QR = 6.5 cm, $\angle P=\angle R={100}^{\circ }$ and $\angle S={75}^{\circ }$.

Q.

What are the conditions that must be satisfied to construct a quadrilateral?

Q.

Is it possible to construct a unique quadrilateral ABCD with AB = 4cm, AD = 6 cm, $\angle ABC={60}^{\circ }$, $\angle DAB={75}^{\circ }$, and $\angle ADC={85}^{\circ }$? If yes, find the value of $\angle BCD$.

1. No, it is impossible

2. yes,

3. yes,

4. yes,

Q. With 2 adjacent sides and a minimum of angles, we can construct a unique quadrilateral.

1. 4
2. 2
3. 3
4. 5

Q.

In a quadrilateral MIST, MI = 3.5 cm, IS = 6.5 cm, Angle M = ${75}^{\circ }$, Angle I = ${105}^{\circ }$ and Angle S = ${120}^{\circ }$. Which line segment should be drawn first?

1. MI

2. IS

3. IM

4. Either IS or MI

Q.

If the measurement of sides of a quadrilateral are given as AB = 4cm, CD = 5 cm, and angles are given as $\angle ABC=$ ${75}^{\circ }$, $\angle BCD=$ ${45}^{\circ }$ and $\angle CDA=$ ${135}^{\circ }$, can you construct a unique quadrilateral ABCD?

1. No

2. With measure of DAB, Yes

3. Yes

4. With measure of BC, Yes

Q. If we have the measurements of 2 adjacent sides and a minimum of ___ angles, we can construct a unique quadrilateral.

1. 2
2. 3
3. 4
4. 5

Q. For constructing a quadrilateral when 2 sides and 3 angles are given, the length of any 2 sides can be sufficient.

1. True
2. False

Q.

During the construction of a quadrilateral for which 2 sides and 3 angles are known, how is the 4th point plotted?

1. Using angle and length

2. Using 2 angles

3. Using only length

4. Using arcs

Q.

In a quadrilateral MIST, MI = 3.5 cm, IS = 6.5 cm, $\angle M$ = ${75}^{\circ }$, $\angle I$ = ${105}^{\circ }$ and $\angle S$ = ${120}^{\circ }$. Which of the given line segments could be drawn first to construct the quadrilateral ?

1. MI

2. IS

3. IM

4. Either IS or MI

Q. Construct a quadrilateral ABCD, when: $\angle A={90}^{\circ }$, AB = 4.6 cm, BC = 5.0 cm, AD = 6.0 cm and CD = 4.2 cm.

Q.

For drawing a quadrilateral when 2 sides and 3 angles are given, the length of any 2 sides can be sufficient.

1. False

2. True

Q.

If we have measurments of 2 adjacent sides and minimum of __ angles, we can construct a unique quadrilateral. Fill in the blank.

Q.

Construct a quadrilateral ABCD in which AB = BC = 3 cm, AD = 5 cm, $\angle A={90}^{\circ }$ and $\angle B={105}^{\circ }.$

Q.

If measure of 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. With the measure of BC, Yes

2. Yes

3. No

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

Q.

What is drawn in the first step in constructing a quadrilateral for which 2 sides and 3 angles are known?

1. Arc

2. Line Segment

3. Triangle

4. None of these

Q.

In a quadrilateral MIST, MI = 3.5 cm, IS = 6.5 cm, Angle M = ${75}^{\circ }$, Angle I = ${105}^{\circ }$ and Angle S = ${120}^{\circ }$. Which line segment should be drawn first?

1. MI

2. IS

3. IM

4. Either IS or MI

Q. Is it possible to construct a unique quadrilateral ABCD with AB = 4cm, AD = 6 cm, $\angle ABC={60}^{\circ }$, $\angle DAB={75}^{\circ }$, and $\angle ADC={85}^{\circ }$? If yes, find the value of $\angle BCD$.

1. No, it is impossible

2. Yes, ${140}^{\circ }$

3. Yes, ${130}^{\circ }$

4. Yes, ${150}^{\circ }$

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. 3
2. 2
3. 4
4. 1

Q. For constructing a quadrilateral when 2 sides and 3 angles are given, the length of any 2 sides can be sufficient.

1. False
2. True