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

Q.

Construct a quadrilateral ABCD in which: $\angle \text{A}={120}^{\circ },\angle \text{B}={60}^{\circ },\angle \text{AB}=4cm,BC=4.5cm\text{and}CD=5cm.$

Q. Construction of quadrilaterals when two adjacent sides and three angles are given:
4. Construct a quadrilateral PQRS in which PQ = 4.5 cm $\angle PQR={120}^{\circ },QR=3.8cm,\angle QRS={100}^{\circ }$ and $\angle QPS={60}^{\circ }.$

Q.

Construct a quadrilateral ABCD, such that AB = BC = CD = 4.4 cm, $\angle B={90}^{\circ }\text{and}\angle C={120}^{\circ }$.

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. PQ
2. QR
3. RS
4. PR

Q. Can a quadrilateral be constructed if the measurement of its any three of the four angles and the length of its any two four sides are given ?
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Q. Construct a quadrilateral NEWS in which NE = 7 cm, EW = 6 cm, $\angle N={60}^{\circ },\angle E={110}^{\circ }$ and $\angle S={85}^{\circ }$.

Q.

2 sides and 3 angles of a quadrilateral that is to be constructed are given. How can you find the location of the 4th point? [1 Mark]

Q. Construct a quadrilateral NEWS in which NE = 7 cm, EW = 6 cm, $\angle N={60}^{\circ },\angle E={110}^{\circ }$ and $\angle S={85}^{\circ }$.

Q.

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

Q.

Construct a quadrilateral ABCD, with AB = 4.0 cm, BC = 4.5 cm, CD = 4.7 cm, $\angle B={60}^{\circ }$ and $\angle A={120}^{\circ }$ [4 MARKS]

Q. Match the following elements that are required for the construction of unique quadrilaterals.

1. 1 diagonal
2. 3 sides
3. 3 angles
4. 2 diagonals

Q.

Construct a quadrilateral ABCD in which AB = 3.6 cm, BC = 5.5 cm, CD = 5 cm, $\angle B={125}^{\circ }$ and $\angle C={80}^{\circ }$ [2 MARKS]

Q. Match the following elements that are required for the construction of unique quadrilaterals.

1. 3 angles
2. 3 sides
3. 2 diagonals
4. 1 diagonal

Q. Construct a quadrilateral NEWS in which NE = 7 cm, EW = 6 cm, $\angle N={60}^{\circ },\angle E={110}^{\circ }$ and $\angle S={85}^{\circ }$.

Q. Match the following elements that are required for the construction of unique quadrilaterals.

1. 2 diagonals
2. 3 angles
3. 3 sides
4. 1 diagonal

Q. Match the following elements that are required for the construction of unique quadrilaterals.

1. 3 angles
2. 1 diagonal
3. 2 diagonals
4. 3 sides

Q. We cannot construct any quadrilateral with less than 5 measurements given.

1. True
2. False

Q. A parallelogram is constructed and named KLMN. LP is perpendicular to KL and ML is the angular bisector of $\angle KLP$. Find the value of $\angle KNM$.

1. ${45}^{\circ }$
2. ${15}^{\circ }$
3. ${30}^{\circ }$
4. ${60}^{\circ }$

Q.

How many quadrilaterals can I construct with the following data: Quadrilateral PQRS with PQ = 4.5 cm, Angle P = ${70}^{\circ }$, Angle Q = ${100}^{\circ }$, Angle R = ${80}^{\circ }$ and Angle S =${80}^{\circ }$.

1. infinite

2. 0

3. 1

4. 2

Q.

Construct a quadrilateral ABCD given that AB = 4 cm, BC = 3 cm, $\angle A={75}^{\circ },\angle B={80}^{\circ }$ and $\angle C={120}^{\circ }$.

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 the value of $\angle QRS$?

1. 

2. 

3. 

4. 

Q.

I construct quadrilateral with 3 sides and 2 included angles being ${75}^{\circ }$ and ${105}^{\circ }$ respectively and no sides are equal. What is the type of quadrilateral I am constructing?

1. Trapezium

2. Square

3. Parallelogram

4. None of these

Q. Match the following elements that are required for the construction of unique quadrilaterals.

1. 2 diagonals
2. 3 sides
3. 3 angles
4. 1 diagonal

Q. Construct a quadrilateral NEWS in which NE = 7 cm, EW = 6 cm, $\angle N={60}^{\circ },\angle E={110}^{\circ }$ and $\angle S={85}^{\circ }$.

Q. I construct a quadrilateral with 3 sides and 2 included angles which are also adjacent angles and their measures are ${75}^{\circ }$ and ${105}^{\circ }$ respectively. No sides are equal and one pair of opposite sides are parallel in this quadrilateral. What is the type of quadrilateral I am constructing?

1. Rhombus
2. Square
3. Trapezium
4. Parallelogram

Q.

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

1. Yes, it is possible

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

3. No, two such quadrilaterals can be constructed

4. No, there can be infinite such quadrilaterals

Q. The acute angle made by the diagonals is:

1. ${74}^{\circ }$
2. ${63}^{\circ }$
3. ${16}^{\circ }$
4. ${37}^{\circ }$

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 the value of $\angle QRS$?

1. 

2. 

3. 

4. 

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. No, two such quadrilaterals can be constructed

2. No, there can be infinite such quadrilaterals

3. With the measure of an extra side, yes

4. Yes, it is possible

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.