Construction of Quadrilateral Given 2 Sides and 3 Consecutive Angles

Q.

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

1. Using 2 angles

2. Using angle and length

3. Using only length

4. Using arcs

Q.

While constructing quadrilateral PQRS with 3 sides and 2 diagonals, which of the following geometric apparatus is not used?

1. Ruler

2. Protractor

3. Compass

4. None of These

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, ${130}^{\circ }$

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

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

Q.

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

Q. Construct the following quadrilaterals
(i) Quadrilateral $\text{DEAR}$
$\text{DE}=4\text{cm}$
$\text{EA}=5\text{cm}$
$\text{AR}=4.5\text{cm}$
$\angle \text{E}={60}^{\circ }$
$\angle \text{A}={90}^{\circ }$
(ii) Quadrilateral $\text{TRUE}$
$\text{TR}=3.5\text{cm}$
$\text{RU}=3\text{cm}$
$\text{UE}=4\text{cm}$
$\angle \text{R}={75}^{\circ }$
$\angle \text{U}={120}^{\circ }$

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. No

3. With measure of BC, Yes

4. Yes

Q.

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

1. True

2. False

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. Yes

2. No

3. With measure of DAB, Yes

4. With measure of BC, Yes

Q.

Given below are the steps for the 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 is wrong?
1:- Draw AB = 3.5 cm.
2:- Construct $\angle DAB={75}^{\circ },\angle ABC={105}^{\circ }$ at B.
3:- Draw BC = 6.5 cm.
4:- At D construct $\angle ADC={120}^{\circ }$.

1. 2

2. 1

3. 3

4. 4

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 $\angle BCD$.
$\left[4Marks\right]$

Q. State whether the following statement is True or False
We can construct a quadrilateral $ABCD$, if AB=$3.6$cm $\angle ABD$=${80}^o$, $BC=4$cm, $\angle BAD={120}^o$

1. True
2. False