4 Sides, 1 Diagonal

Q.

If there is a quadrilateral ABCD and you have measures of any three sides and two diagonals of the quadrilateral ABCD, can you construct it?

1. No, it is impossible

2. Yes, definitely

3. With a measure of one angle too, yes

4. I can construct half quadrilateral

Q. Construct a quadrilateral ABCD in which AB = 4.2 cm, BC = 6 cm, CD = 5.2 cm, DA = 5 cm and AC = 8 cm.

Q. PQRS is a quadrilateral. PQ = 4cm, QR = 6 cm, SR = 5 cm,
PS = 5.5 cm and PR = 7 cm.
The steps for construction are :

Step 1: Draw a line segment PR of length 7 cm.
Step 2: Draw an arc of length 4 cm from P and another arc of length 6 cm from the point R.
Step 3: Mark the intersecting point of the arcs be Q. Join Q to P and R.

What is the next step?

1. Draw an arc of length 5.5 cm from P and another arc of length 5 cm from R.
2. Mark the intersecting point of the arcs to be S.
3. Join S to P and R.
4. The quadrilateral PQRS is constructed.

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

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

Q. ABCD is a quadrilateral. If AB, BC, CA and $\angle$ABC is known, which of the following parameter is required for the construction of the quadrilateralABCD.

1. BD
2. AC
3. $\angle BAC$
4. AD

Q.

There is a quadrilateral PLAY with PL = 3cm, LA = 4cm, AY = 4.5 cm, PY = 2cm. Which of the following values of LY is not possible?

1. 2

2. 3

3. 6

4. None of these

Q.

Question 2
Construct the Quadrilateral GOLD where

OL=7.5 cm, GL=6cm, LD=5cm, OD=10 cm

Q.

A student wants to construct a quadrilateral ABCD with the measurements AB = 3cm, BC = 4cm, CD = 4.5cm, AD = 2cm and BD = 6cm but he could not construct it .What could be the reason?

1. In ΔABD, sum of sides AB and AD is less than the third side BD

2. Length of a diagonal can not be less than the length of the sides of the quadrilateral

3. In ΔBCD, sum of the sides BC and CD is greater than the third side BD

4. A quadrilateral cannot be constructed if the measurements of four sides and a diagonal is given

Q.

Construct the following quadrilateral: Quadrilateral $\text{MORE}$, $\text{MO = 6 cm, OR = 4.5 cm, ∠M = 60°, ∠O = 105°, ∠R = 105°}$

Q. If two diagonals are given, which of the following quadrilaterals can be constructed?

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

Q.
A rhombus ABCD is to be constructed with side AD = 5 cm. Which of the following dimensions must also be specified to construct the rhombus?

Q.

Question 2
Construct the Quadrilateral JUMP where

JU =3.5 cm, UM = 4 cm, MP = 5cm, PJ=4.5 cm, PU= 6.5 cm

Q.

Question 1
Construct the Quadrilateral LIFT where
LI=4 cm, IF = 3 cm, TL = 2.5 CM, LF = 4.5 cm , IT = 4 cm

Q.

A rhombus ABCD is to be constructed with side AB = 5 cm. Which of the following dimensions must also be specified to construct the rhombus?

1. Given information is enough to construct the rhombus.

2. AC

3. BC

4. AD

Q.

When we draw quadrilateral which line we take base line

Q. A quadrilateral ABCD is to be constructed with AB = 2 cm, BC = 3.5 cm, CD = 3 cm and DA = 4 cm. Which of the following value given for BD is not possible?

1. 3 cm
2. 7 cm
3. 5 cm
4. 4 cm

Q. If the measure of sides of a quadrilateral are given as AB = 7cm, AD = 5 cm and BD = 10 cm. Can you draw a quadrilateral ABCD?

1. Yes
2. No
3. Yes, if BC is given.
4. Yes, if BC and CD is given.

Q. In a quadrilateral ABCD, AB = 7 cm, BC = 5 cm, AC = 9 cm, AD = 6 cm, CD = 2 cm. Which of the following options is true about the construction of a quadrilateral ABCD?

1. It is possible to draw the quadrilateral
2. It is not possible to draw the quadrilateral since AD + DC < AC
3. It is possible to draw the quadrilateral since AD + DC < AC
4. None of these

Q. PQRS is a quadrilateral. PQ = 4cm, QR = 6 cm, SR = 5 cm,
PS = 5.5 cm and PR = 7 cm.
The steps for construction are :

Step 1: Draw a line segment PR of length 7 cm.
Step 2: Draw an arc of length 4 cm from P and another arc of length 6 cm from the point R.
Step 3: Mark the intersecting point of the arcs be Q. Join Q to P and R.

What is the next step?

1. Draw an arc of length 5.5 cm from P and another arc of length 5 cm from R.
2. Mark the intersecting point of the arcs to be S.
3. Join S to P and R.
4. The quadrilateral PQRS is constructed.

Q. State the following statement is True or False
We can construct a quadrilateral if only $3$ sides and one angle are given

1. True
2. False

Q.

A student wants to construct a quadrilateral ABCD with the measurements AB = 3cm, BC = 4cm, CD = 4.5cm, AD = 2cm and BD = 6cm but he could not construct it .What could be the reason?

1. A quadrilateral cannot be constructed if the measurements of four sides and a diagonal is given

2. Length of a diagonal can not be less than the length of the sides of the quadrilateral

3. In ΔBCD, sum of the sides BC and CD is greater than the third side BD

4. In ΔABD, sum of sides AB and AD is less than the third side BD

Q. PQRS is a quadrilateral. PQ = 4cm, QR = 6 cm, SR = 5 cm,
PS = 5.5 cm and PR = 7 cm.
The steps for construction are :

Step 1: Draw a line segment PR of length 7 cm.
Step 2: Draw an arc of length 4 cm from P and another arc of length 6 cm from the point R.
Step 3: Mark the intersecting point of the arcs be Q. Join Q to P and R.

What is the next step?

1. Join S to P and R.
2. Draw an arc of length 5.5 cm from P and another arc of length 5 cm from R.
3. Mark the intersecting point of the arcs to be S.
4. The quadrilateral PQRS is constructed.

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.

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 $\angle DAB$, Yes

4. With measurement of BC, Yes

Q. Let us say you are required to construct a quadrilateral $ABCD$ where the measurements are $AB=5\text{cm},BC=3\text{cm},\angle A=120°,\angle B=110°,$ and $\angle C=130°$.
A quadrilateral with the above specifications will be in the shape of:

1. Cannot construct a quadrilateral with the given specifications
2. Parallelogram
3. Square
4. Trapezium

Q.

Can we draw a quadrilateral ABCD with following specifications; AB = 3 cm, BC = 5 cm, AD = 4 cm, CD = 7 cm and BD = 8 cm?

1. With the measure of another diagonal, Yes

2. Yes definitely

3. No, it is impossible

4. With the measure of extra angle, Yes

Q. The measurements of 4 sides and 1 diagonal are given. The simplest way to construct a quadrilateral with the above information will be ____.

1. constructing two triangles and joining them
2. to start drawing with the given sides
3. to start with diagonals and construct triangles above and below the diagonal.
4. construction not possible

Q. What is the minimum number of measurements required to construct a parallelogram?

1. 4
2. 2
3. 3
4. 5

Q. Question 192
Construct a quadrilateral BEAR in which BE = 6 cm, EA = 7 cm, RB = RE = 5 cm and BA = 9 cm. Measure its fourth side.

Q.

Construct a quadrilateral ABCD in which AB = 5.5 cm, AD = 4.4 cm, CD = 6.5 cm, AC = 6.5 cm, and BD = 7.1 cm. [4 MARKS]