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

Q.

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

Q. To construct a unique quadrilateral we should have a minimum measurement of 3 sides and included angles.

1. 3
2. 2
3. 5

Q.

Construct a quadrilateral ABCD in which AB = 4 cm, AC = 5 cm, AD = 5.5 cm and $\angle ABC=\angle ACD={90}^{\circ }$.

Q.

Construct a quadrilateral PQRS in which PQ = 6 cm, QR = 5.6 cm, RS = 2.7 cm, $\angle Q={45}^{\circ }$ and $\angle R={90}^{\circ }$.

Q.

Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 5 cm, CD = 4.6 cm, $\angle B={125}^{c}ircand\angle C={60}^{\circ }$.

Q. Question 186
Construct a trapezium ABCD in which $AB\parallel DC,\angle A={105}^{\circ }$, AD = 3 cm, AB = 4 cm and CD = 8 cm.

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 PQRS, in which PQ=3.5 cm, QR=2.5 cm, RS=4.1 cm, $\angle Q={75}^{\circ }$ and $\angle R={120}^{\circ }$.

Q. Construct a quadrilateral $DEAR$ with $DE=6cm,EA=5cm,AR=5.5cm,RD=5.2cm$ and $DA=10cm$. Also find its area.

Q.

Construct a quadrilatera ABCD, where AB=4.2 cm, BC=3.6 cm, CD=4.8 cm, $\angle B={30}^{\circ }$ and $\angle C={150}^{\circ }$

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. According to the construction shown in the diagram below, what do we call segment $\overline{CD}$?

1. bisector of $\angle C$
2. perpendicular bisector of segment $\overline{AB}$
3. median to side $\overline{AB}$
4. altitude to side $\overline{AB}$

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

Q.

Construct a quadrilateral ABCD in which AD=3.5 cm, AB=4.4 cm, BC=4.7 cm, $\angle A={125}^{\circ }$ and $\angle B={120}^{\circ }$

Q. Construction of a unique quadrilateral is possible if we have the measurement of 3 sides and ___ included angle(s).

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

Q. Question 76
Fill in the blanks to make the statements true.​​​​​​​
​​​​​​​A quadrilateral can be constructed uniquely if its three sides and ___ angles are given.

Q.

Construct a quadrilateral ABCD, in which AB=6 cm, BC=4 cm, CD=4 cm, $\angle B={95}^{\circ }$ and $\angle C={90}^{\circ }$

Q.

Construct a quadrilateral PQRS in which $\angle Q={45}^{\circ }$, $\angle R={90}^{\circ },QR=5cm$, PQ=9 cm and RS=7 cm.

Q.

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

Q. ABCD ia quadrilateral, where AB = 7 cm, BC = 6 cm, AD = 8 cm, $\angle A$ = 60° and $\angle B$ = 90°. The following are the steps of construction.

$\to$Draw a line segment AB = 7 cm.
$\to$Make angles 60° and 90° at A and B respectively and extend the lines.
$\to$With A as the centre and radius 8 cm we construct an arc on the extended lines.
$\to$Mark the points C and D.
$\to$Join the points D and C to obtain the required quadrilateral ABCD.

Find the missing step.

1. With B as the centre and radius 6 cm we make an arc on the extended line.
2. Quadrilateral ABCD is hence obtained.
3. Construct 60° and 90° at the points A and B respectively.
4. No steps are missed.

Q.

Construct a quadrilateral $JUMP$, when: $JU=3.5$ cm, $UM=4$ cm, $MP=5$ cm, $PJ=4.5$ cm and $PU=6.5$ cm

Q. In a quadrilateral $ABCD,AB=AC=10cm$ and $DB=DC=5cm$. Its diagonals intersect each other at ${90}^o$.what type of quadrilateral is it.

1. Kite
2. Trapezium
3. Rhombus
4. Rectangle

Q. Construct a quadrilateral PQRS, where $\dot{PQ}=7.7cm,QR=6.8cm,RS=5.1cm,SP=3.6cm$ and $\angle R={120}^{\circ }$.

Q. Construct the following quadrilaterals:

Q. Shubam was given a task of rearranging the steps for the construction of quadrilaterals. The data given was, PS = 4 cm, SR = 5 cm, RQ = 6 cm $\angle PSR$ = 100° and $\angle QRS$ = 120°. Find the correct order.
(a)
(b)(c)(d)

1. (c), (a), (b), (d)
2. (c), (d), (a), (b)
3. (d), (c), (a), (b)
4. (c), (d), (b), (a)

Q. Construct a quadrilateral $ABCD$ with $AB=2.5cm,BC=3.5cm,CD=4.5cm,\angle A={90}^o$ and $\angle B={120}^o$.

Q. Construct a cyclic quadrilateral $PQRS$ with $PQ=5.5$ cm, $QR=4.5$ cm, $\angle QPR={45}^o$ and $PS=3$ cm.

Q. Constant a quadrilateral $ABCD$, where $AB=4cm,BC=5cm,CD=6.5cm$ and $\angle B={105}^o$ and $\angle C={80}^o$

Q.

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

Q. Construct a quadrilateral ABCD with $AB=6.5\text{cm}$, $AD=5\text{cm}$, $CD=5\text{cm}$, $\angle$ BAC = ${40}^{\circ }$ and $\angle$ ABC = ${50}^{\circ }$ , and also find its area.