Construction of Quadrilateral When 3 Sides and 2 Angles Are Given

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. 3

2. 2

3. 4

4. 1

Q. Construct the following quadrilaterals
(i) Quadrilateral $MORE$
$MO=6cm$
$OR=4.5cm$
$\angle M={60}^{\circ }$
$\angle O={105}^{\circ }$
$\angle R={105}^{\circ }$

Q.

Is it possible to construct a unique quadrilateral ABCD with AB = 3.6 cm, BC = 4 cm, AD= 5 cm, $\angle$ABC = ${80}^{\circ }$ and $\angle$ BAD = ${120}^{\circ }$?

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

2. Yes, it is possible

3. No, two such quadrilaterals can be constructed

4. No, there can be infinite such quadrilaterals

Q.

Question 2
Construct the Quadrilateral TRUE
TR=3.5 cm, RU=3cm, UE=4cm, $\angle R={75}^{\circ },\angle U={120}^{\circ }$

Q.

Construct a quadrilateral ABCD given that AB = 8 cm, BC = 8 cm, CD = 10 cm, AD = 10 cm and $\angle B={45}^{\circ }.$

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 MORE where MO = 6 cm , OR = 4.5 cm, $\angle M={60}^{\circ },\angle O={105}^{\circ },\angle R={105}^{\circ }$.

Q.

Question 1
Construct the Quadrilateral DEAR where
DE=4cm, EA=5cm, AR=4.5cm, $\angle E={60}^{\circ },\angle A={90}^{\circ }$

Q.

Is it possible to construct a unique quadrilateral ABCD with AB = 5cm, BC = 6cm, CD= 7cm , $\angle$ ABC = ${45}^{\circ }$ 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 one more side, yes

Q. Ajay is constructing a quadrilateral ABCD where AB = 5 cm, BC = 3 cm, $\angle$DAB = 120°, $\angle$ABC = 110° and $\angle$DCB = 90°.
He is constructing as follows:

Step 1:
Step 2:
What will be step 3?

1. 
2. 
3. 
4. None of the above.

Q. Using ruler and compass only, construct the quadrilateral ABCD, having given AB = $5$ cm, BC = $2.5$ cm, CD = $6$ cm, angle BAD = ${90}^{\circ }$ and the diagonal AC = $5.5$ cm.

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.

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. A minimum of five measurements are required to construct a quadrilateral.

1. True
2. False

Q.

If you have AB = 3 cm, BC = 4 cm, CD = 5 cm & and DA = 6 cm, can you draw the quadrilateral ABCD? If you can, will this quadrilateral be unique?

1. Yes; Yes

2. Yes; No

3. No; Yes

4. No; No

Q.

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

Q.

If you are given AB = 5 cm, BC = 6 cm, CD = 7 cm, DA = 6 cm and $\angle ABC$ = ${60}^{\circ }$, then it is possible to draw the quadrilateral ABCD.

1. False

2. True

Q.

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

1. Yes, it is possible

2. No, two such quadrilaterals can be constructed

3. With the measure of an extra side, yes

4. No, there can be infinite such quadrilaterals

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 should be taken as the base of the quadrilateral?

1. RS
2. PR
3. PQ
4. QR

Q.

Is it possible to construct a unique quadrilateral ABCD with AB = 3.6 cm, BC = 4 cm, AD= 5 cm, $\angle$ABC = ${80}^{\circ }$ and $\angle$ BAD = ${120}^{\circ }$?

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.

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.