# Construction of Parallelogram When Two Adjacent Sides and the Included Angles Are Given.

## Trending Questions

**Q.**

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

**Q.**

Construct a parallelogram ABCD, if :

(i) AB = 3.6 cm, BC = 4.5 cm and ∠ABC=120∘.

(ii) BC = 4.5 cm, CD = 5.2 cm and ∠ADC=75∘.

(iii) AD = 4 cm, DC = 5 cm and diagonal BD = 7 cm.

(iv) AB = 5.8 cm, AD = 4.6 cm and diagonal AC = 7.5 cm.

(v) diagonal AC = 6.4 cm, diagonal BD = 5.6 cm and angle between the diagonals is 75∘.

(vi) lengths of diagonals AC and BD are 6.3 cm and 7.0 cm respectively, and the angle between them is 45∘.

(vii) lengths of diagonals AC and BD are 5.4 cm and 6.7 cm respectively and the angle between then is 60∘.

**Q.**

Construct a quadrilateral ABCD, where AB = 4 cm, BC = 5 cm, CD = 6.5 cm and Angle B = 105∘ and Angle C = 80∘.

**Q.**

Construct Parallelogram HEAR where HE = 5 cm, EA = 6 cm, ∠R=85∘. [4 MARKS]

**Q.**

Construct a parallelogram ABCD in which BC = 5 cm, ∠BCD=120∘ CD = 4.8 cm.

**Q.**

Draw a parallelogram ABCD, with AB = 6 cm, AD = 4.8 cm and ∠DAB=45∘. Draw the perpendicular bisector of side AD and let it meet AD at point P. Also draw the diagonals AC and BD ; and let they interest at point O. Join O and P. Measure OP.

**Q.**

Construct a quadrilateral ABCD given AB = 5.6 cm, BC = 4.1, CD = 4.4 cm, AD = 3.3 cm and ∠A=75∘ [3 MARKS]

**Q.**Construction of quadrilaterals when three sides and two included angles are given:

3. Construct a quadrilateral ABCD in which AB=3.6cm, ∠ABC=80∘, BC=4cm, ∠BAD=120∘ and AD = 5 cm.

**Q.**

Using ruler and compasses only, construct a parallelogram ABCD, in which : AB = 6 cm, AD = 3 cm and ∠DAB=60∘. In the same figure draw the bisector of angle DAB and let it meet DC at point P. Measure angle APB.

**Q.**Question 187

Construct a parallelogram ABCD in which AB = 4 cm, BC = 5 cm and ∠B=60∘.

**Q.**

A parallelogram has sides of 12 cm and 8 cm. If the distance between the 12 cm sides is 5 cm. Find the distance between 8 cm sides. [4 MARKS]

**Q.**

State whether True or False: Each point on a perpendicular bisector is such that it forms an isosceles triangle with the given line segment.

False

True

**Q.**Construct the parallelograms with the given measurements and find their area.

GAIN, GA = 7.5 cm, GI = 9 cm and ∠GAI – 100°

[5]

**Q.**Draw an ∠ BAC of measure 50∘ such that AB=5cm and AC=7cm. Through C draw a line parallel to AB and through B draw a line parallel to AC, intersection each other at D. Measure BD and CD.

**Q.**In the diagram, KLMN is a constructed parallelogram. The value of ∠KLM is

- 15∘
- 30∘
- 45∘
- 60∘

**Q.**Construct a parallelogram PQRS, given PQ=5 cm, QR=4 cm and ∠PQR=70o and calculate the perimeter of the parallelogram.

- 12 cm
- 18 cm
- 16 cm
- None of these

**Q.**Construct a parallelogram PQRS , where PQ =5.2 cm , PR = 6 cm and QS = 6.4 cm.

**Q.**If KLMN is a constructed parallelogram, what is the value of ∠KLM?

- 15o
- 450
- 30o
- 60o

**Q.**Using ruler and compasses only, construct a parallelogram ABCD using the following data :

AB = 6 cm, AD = 3 cm, and ∠DAB=45∘. If the bisector of ∠DAB meets DC at P, prove that ∠APB is right angle.

**Q.**Question 193

Construct a parallelogram POUR in which PO = 5.5 cm, OU = 7.2 cm and ∠O=70∘.

**Q.**

We have a parallelogram ABCD with AC and BD as diagonals. In Parallelogram ABCD, ∠ABC=130∘, ∠DAC=15∘, ∠CAB=25∘, AB = 5 cm and CD = 7 cm. Can we construct this parallelogram?

With ADC, yes

No, it is impossible

With AC yes

Yes, of course

**Q.**ABCD is a parallelogram. AB=8cm, AD=4cm, ∠B=120o

a. What is ∠A

b. What is the perpendicular distance from D to AB?

c. What is the area of ABCD?

**Q.**Construct a quadrilateral ABCD, when: AD = AB = 4 cm, BC = 2.8 cm, CD = 2.5 cm and angleBAD=45∘.

**Q.**

Construct the quadrilaterals with the given measurements. And write steps of construction.

Quadrilateral ABCD with AB=5.5cm, BC=3.5cm, CD=4cm, AD=5cm and ∠A =45o.

**Q.**For construction of parallelogram ABCD such that AD=4.5 cm, AB=5 cm and ∠A=70o, steps for its construction is given below in jumbled form. Which would be the third step of construction?

2) Draw an axis AX and mark AB=5 cm on it and draw a ray AY such that ∠A=70o

3) Mark point D on AY such that AD=4.5 cm

4) Draw arcs of radius 5 cm as centre D and with radius 4.5 cm as centre B which intersect at point C

- 3
- 2
- 4
- 1

**Q.**Construct a parallelogram ABCD, with AB=6 cm, BC=4 cm and ∠ABC=60∘. Then the perimeter of the parallelogram is:

- 10 cm
- 30 cm
- 20 cm
- 15 cm

**Q.**

It is possible to draw a unique parallelogram with side lengths 4 cm and 9 cm.

- True
- False

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

**Q.**Construct parallelogram ABCD with the following measurements:

AD=4.2cm, DC=5.8cm, ∠D=43o

**Q.**Construct a parallelogram PQRS, given PQ=5 cm, QR=4 cm and ∠PQR=70o and calculate ∠QRS.

- 90o
- 105o
- 110o
- None of these