3 Sides, 2 Included Angles

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. 2

2. infinite

3. 0

4. 1

Q. Ram is constructing a quadrilateral DEAR. He knows the measurements DE = 5 cm, EA = 4 cm, RA = 6 cm, $\angle$ E = 60° and $\angle$ A = 110°. What will be his first step of construction?

1. Draw a line segment EA of length 4 cm.
2. Draw 60° at the point E.
3. Draw 110° at the point A.
4. Draw 60° at the point D.

Q.

Construct the following quadrilateral: Parallelogram $\text{MORE}$ where $\text{OR = 6 cm}$, $\text{ER = 4.5 cm}$ and $\text{EO = 7.5 cm}$.

Q. We can construct a quadrilateral, if the measure of 3 sides and is / are given.

1. 1 adjacent angle
2. 1 diagonal
3. 1 included angle
4. 2 included angles

Q. Construct a quadrilateral REAL, where RE=6cm, EA=5cm and angle R= 120 degree.

Q. The following quadrilateral LMNO can be constructed when _______ is given.

1. 1 side, 4 angles
2. 4 sides, 1 angle
3. 3 sides, 2 included angles
4. 2 sides, 3 included angles

Q. Jack wanted to construct a quadrilateral TRUE with the following measurements. TR = 3.5 cm, RU = 3 cm, UE = 4 cm, $\angle R=75°$ and $\angle U=120°$. Find which of the following is the correct one.

1. 
2. 
3. 
4. 

Q.

Draw the following:

A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm.

Q. Construct a parallelogram PQRS in which QR = 6 cm, PQ = 4 cm and ∠PQR = 60° cm.

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

Q. The total perimeter of a quadrilateral ABCD is 18 cm. The opposite sides are equal and parallel. The adjacent sides are 1 cm more than the other. One of the angles of the quadrilateral ABCD measures 60°. Construct the quadrilateral ABCD.

1. 
2. 
3. 
4. 

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. Construct a cyclic quadrilateral $PQRS$ whose side $PQ=5.0cm$, $QS=6.0cm$, $PS=3.5cm$ and $RS=5.0cm$

Q. Construct the Parallelogram MORE where OR = 6 cm, RE = 4.5 cm, EO = 7.5 cm.

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

Q. Construct a parallelogram PQRS where the $\angle Q=120°$, PR is the diagonal, $\angle RPQ=30°$.

1. We cannot construct the quadrilateral PQRS.
2. 
3. 
4. Data insufficient

Q. Given a $△ABC$. From this triangle, construct a quadrilateral ABCD such that AC will be the diagonal, $\angle ACD=90°$, CD = 2.3 cm and measure the length of AD.

1. 5.5 cm
2. 10 cm
3. 1 cm
4. 8 cm

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