Construction of Quadrilateral (2 Sides and 3 Angles)

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 ine segments could be drawn first to construct the quadrilateral ?

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, $\angle ABC=60°$ , $\angle DAB=75°$, $\angle ADC=85°$? If yes, construct it and find $\angle BCD$.

1. yes, ${130}^{\circ }$

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

3. yes, ${150}^{\circ }$

4. No, it is impossible

Q. Question 75

___ measurements can determine a quadrilateral uniquely.

Q. Question 129
State whether the statements are True or False.
A quadrilateral can be constructed uniquely, if three angles and any two included sides are given.

Q.

We have a parallelogram ABCD with AC and BD as diagonals. In Parallelogram ABCD, $\angle$ABC= ${110}^{\circ }$, $\angle$DAC = ${15}^{\circ }$, $\angle$CAB= ${25}^{\circ }$, AB = 5 cm, CD = 7 cm. Can we construct this parallelogram?

1. With AC yes

2. No, it is impossible

3. Yes, of course

4. With ADC, yes

Q.

In a quadrilateral MIST where 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. Either IS or MI

2. MI

3. IS

4. IM

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.

Whether is it possible to construct a unique quadrilateral ABCD with AB = 6cm, AD = 7cm, $\angle$ABC = ${30}^{\circ }$ , $\angle$DAB = ${60}^{\circ }$,

$\angle$ADC = ${80}^{\circ }$ ? If yes, construct it and find $\angle$BCD.

1. No, it is impossible

2. Yes, 130^o

3. Yes, 190^o

4. Yes, 140^o

Q. For drawing a quadrilateral when 2 sides and 3 angles are given, the length of any 2 sides is sufficient. State whether true or false.

1. True
2. False

Q. Construct $\Delta$ABC, given $m\angle A={60}^o$, $m\angle B={30}^o$ and $AB=5.8$ cm.

Q.

If measure of sides of a quadrilateral are given as AB = 4cm, CD = 5cm, and angles are given as $\angle ABC={75}^{\circ },\angle BCD={45}^{\circ }and\angle CDA={135}^{\circ }$, then what additional information is required to construct a quadrilateral ABCD?

1. Yes

2. No

3. With the measure of BC, Yes

4. With the measure of ∠DAB, Yes

Q.

If we have measures of 2 adjacent sides and minimum __ angles, we can construct a unique quadrilateral.

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. 1
3. 3
4. 2

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

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

Q.

If we have measures of 2 adjacent sides and minimum __ angles, we can construct a unique quadrilateral.

Q.

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

1. With measure of $\angle$DAB, Yes

2. With measure of BC, Yes

3. Yes

4. No