Construction of a Quadrilateral When Two Diagonals and Three Sides Are Given

Q.

Construct Quadrilateral GOLD with OL=7.5 cm, GL= 6 cm, GD = 6 cm, LD = 5 cm, OD = 10 cm. [3 MARKS]

Q.

Construct a quadrilateral PQRS where PQ = 4 cm, QR = 6 cm, RS = 5 cm, PS = 5.5 cm and PR = 7 cm.[3 MARKS]

Q.

Construct a quadrilateral ABCD in which AB = 4.4 cm, BC = 4 cm, CD = 6.4 cm, DA = 2.8 cm and BD = 6.6 cm. [3 MARKS]

Q.

Construct a quadrilateral ABCD in which BC =7.5 cm, AC=AD= 6 cm, CD=5 cm, BD=10 cm.

Q.

Construct a quadrilateral ABCD in which AB = 3.4 cm, CD = 3 cm, DA = 5.7 cm, AC = 8 cm and BD = 4 cm.

Q.

Construct a quadrilateral $ABCD,$ when $AB=3cm,CD=3cm,DA=7.5cm,AC=8cm,BD=4cm.$

Q.

Construct a quadrilateral PQRS in which QR = 7.5 cm, PR = PS = 6 cm, RS = 5 cm and QS =10 cm. Measure the fourth side.

Q. Steps for the construction of a quadrilateral PQRS in which PQ = 4 cm, QR = 3 cm, PS = 2.5 cm, PR = 4.5 cm and QS = 4 cm are given below.

Choose the correct order.

1: Draw a line segment PQ = 4 cm.

2: With 4.5 cm from P draw an arc.

3: Take 2.5 cm from P and draw an arc.

4: From Q take radius 3 cm and cut the arc drawn in step 2. Let the point of intersection be R.

5: Take 4 cm from Q and cut the arc drawn in step 4. Let the point of intersection of arcs be S. Join SR

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

Q.

Question 3
Construct the Rhombus BEND where
BN=5.6 cm, DE=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.

Construct a quadrilateral ABCD in which AB = 3.6 cm, BC = 3.3 cm, AD = 2.7 cm, diagonal AC = 4.6 cm and diagonal BD = 4 cm.

Q.

A student attempted to draw a quadrilateral PLAY such that

PL=3 cm, LA= 4 cm, AY=4.5 cm, PY=2 cm, and LY=6 cm. But he was not able to draw it. Why? [1 Mark]

Q.

Construct a quadrilateral ABCD in which AB = 3.8 cm, BC=3.0 cm, AD=2.3 cm, AC=4.5 cm, and BD =3.8 cm.

Q.

If you have to draw the quadrilateral ABCD given below, what all measurements will you need to draw the quadrilateral ABCD? The measurements are given in following options which of the options can help to draw ABCD?

1. AB, BC, CD, DA

2. AB, BC, CD, DA, BD

3. AB, BC, CD, AC, BD

4. Both options B & C

Q. Girish constructed a quadrilateral PQRS, where sides PS = 5cm, SR = 3 cm, and QR = 3.5 cm, diagonals PR = 5cm and QS = 8 cm. Following is the steps of construction.

Step 1: Draw a line segment PR of length 5 cm.

Step 2: With P as center, draw an arc of radius 5 cm and R as center, draw an arc of radius 3 cm.

Step 3: Mark the intersecting point of the arcs to be S and join S to P and R.

Find the next step.

1. Quadrilateral PQRS is hence constructed.
2. Similarly from R, draw an arc of radius 3.5 cm. Mark the intersecting point to be Q.
3. Join Q to P and R.
4. To the opposite side of PR, keeping S as the center, draw an arc of radius 8 cm.

Q. If DC = 7.3 cm, one of the angles is ${60}^{\circ }$ and the diagonals bisect each other at ${90}^{\circ }$, then which of the following figures can be constructed ?

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

Q.

Question 2
Construct the Quadrilateral GOLD where

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

Q.

Question 4
Construct the Rhombus BEST where
BE = 4.5 cm, ET = 6 cm

Q.

Question 3
Construct the Rhombus BEND where
BN=5.6 cm, DE=6.5 cm

Q.

A quadrilateral ABCD has AB = 7 cm, BC = 4 cm, CD = 5 cm, ∠B = 80^o and ∠C = 100^o. To construct the quadrilateral ABCD, the first step is to draw AB = 7 cm. Which of the following will be the second step?

1. Draw a ray ABX making an angle of 80^o.

2. Draw BC = 4 cm

3. Draw CD = 5 cm.

4. Draw a ray ABX making an angle of 100^o

Q.

Construct a quadrilateral ABCD given AD=3.5cm, BC=2.5 cm, CD=4.1 cm, AC=7.3 cm, and BD=3.2 cm.

Q. Question 127
State whether the statements are True or False.
A quadrilateral can be drawn, if three sides and two diagonals are given.

Q.

Construct a quadrilateral $ABCD$ in which $AB=4.4cm,$ $BC=4cm,$ $CD=6.4cm,DA=2.8cm$ and $BD=6.6cm.$ [ $3$ MARKS]

Q. ABCD is a quadrilateral and the measure of AB, BC , AD and AC are known. Which of the following parameter required for the construction of a unique quadrilateral ABCD ?

1. $\angle BAC$
2. $\angle BCA$
3. $\angle ADB$
4. $BD$

Q.

We can construct an unique quadrilateral ABCD with AB = 4 cm, BC = 6 cm, AC = 7 cm, CD = 5 cm and BD = 8 cm.

1. True

2. False

Q.

Question 2
Construct the rhombus whose diagonals are 5.2 cm and 6.4 cm.

Q. Construct the quadrilateral $DEFG$ such that $l\left(DE\right)=4.5$ cm, $l\left(EF\right)6.5$ cm, $l\left(DG\right)=5.5$ cm, $l\left(DF\right)=7.2$ cm, $l\left(EG\right)=7.8$ cm.

Q. We can construct a parallelogram if the lengths of two diagonals are given.

1. True
2. False

Q. If DC = 7.3 cm, one of the angles is ${60}^{\circ }$, and the diagonals bisect each other at ${90}^{\circ }$, then which of the following figures can be constructed?

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

Q. Construct a quadrilateral $ABCD$ with $AB=3$ cm, $BC=7$ cm, $CD=9$ cm, $CA=11$ cm, $BD=13$ cm.