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

Q.

Construct a parallelogram PQRS in which QR = 6cm, PQ = 4 cm and $\angle PQR={60}^{\circ }$

Q.

Construct a parallelogram ABCD, if :

(i) AB = 3.6 cm, BC = 4.5 cm and $\angle \text{ABC}={120}^{\circ }.$

(ii) BC = 4.5 cm, CD = 5.2 cm and $\angle \text{ADC}={75}^{\circ }.$

(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 ${75}^{\circ }$.

(vi) lengths of diagonals AC and BD are 6.3 cm and 7.0 cm respectively, and the angle between them is ${45}^{\circ }$.

(vii) lengths of diagonals AC and BD are 5.4 cm and 6.7 cm respectively and the angle between then is ${60}^{\circ }$.

Q.

Construct a quadrilateral ABCD, where AB = 4 cm, BC = 5 cm, CD = 6.5 cm and Angle B = ${105}^{\circ }$ and Angle C = ${80}^{\circ }$.

Q.

Construct Parallelogram HEAR where HE = 5 cm, EA = 6 cm, $\angle R={85}^{\circ }$. [4 MARKS]

Q.

Construct a parallelogram ABCD in which BC = 5 cm, $\angle BCD={120}^{\circ }$ CD = 4.8 cm.

Q.

Draw a parallelogram ABCD, with AB = 6 cm, AD = 4.8 cm and $\angle \text{DAB}={45}^{\circ }$. 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 $\angle A={75}^{\circ }$ [3 MARKS]

Q. Construction of quadrilaterals when three sides and two included angles are given:
3. Construct a quadrilateral ABCD in which $AB=3.6cm,\angle ABC={80}^{\circ },BC=4cm,\angle BAD={120}^{\circ }$ and AD = 5 cm.

Q.

Using ruler and compasses only, construct a parallelogram ABCD, in which : AB = 6 cm, AD = 3 cm and $\angle DAB={60}^{\circ }$. 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 $\angle B={60}^{\circ }$.

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.

1. False

2. True

Q. Construct the parallelograms with the given measurements and find their area.
GAIN, GA = 7.5 cm, GI = 9 cm and ∠GAI – 100°
$\left[5\right]$

Q. Draw an $\angle$ BAC of measure ${50}^{\circ }$ such that $AB=5$cm and $AC=7$cm. 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 $\angle$KLM is

1. ${15}^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q. Construct a parallelogram $PQRS$, given $PQ=5$ cm, $QR=4$ cm and $\angle PQR={70}^o$ and calculate the perimeter of the parallelogram.

1. $12$ cm
2. $18$ cm
3. $16$ cm
4. 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 $\angle KLM$?

1. ${15}^o$
2. ${45}^0$
3. ${30}^o$
4. ${60}^o$

Q. Using ruler and compasses only, construct a parallelogram ABCD using the following data :
AB = $6$ cm, AD = $3$ cm, and $\angle DAB={45}^{\circ }$. If the bisector of $\angle DAB$ meets DC at P, prove that $\angle APB$ is right angle.

Q. Question 193
Construct a parallelogram POUR in which PO = 5.5 cm, OU = 7.2 cm and $\angle O={70}^{\circ }$.

Q.

We have a parallelogram ABCD with AC and BD as diagonals. In Parallelogram ABCD, $\angle ABC={130}^{\circ }$, $\angle DAC={15}^{\circ }$, $\angle CAB={25}^{\circ }$, AB = 5 cm and CD = 7 cm. Can we construct this parallelogram?

1. With ADC, yes

2. No, it is impossible

3. With AC yes

4. Yes, of course

Q. $ABCD$ is a parallelogram. $AB=8cm,AD=4cm,\angle B={120}^o$
a. What is $\angle A$
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 $angleBAD={45}^{\circ }$.

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 $\angle A$ $={45}^o$.

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

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

Q. Construct a parallelogram $ABCD$, with $AB=6cm,BC=4cm$ and $\angle ABC={60}^{\circ }$. Then the perimeter of the parallelogram is:

1. $10cm$
2. $30cm$
3. $20cm$
4. $15cm$

Q.

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

1. True
2. False

Q. Construct a parallelogram $PQRS$ in which $QR=6cm,PQ=4cm$ and $\angle PQR={60}^{\circ }$.

Q. Construct parallelogram $ABCD$ with the following measurements:
$AD=4.2cm$, $DC=5.8cm$, $\angle D={43}^o$

Q. Construct a parallelogram $PQRS$, given $PQ=5$ cm, $QR=4$ cm and $\angle PQR={70}^o$ and calculate $\angle QRS$.

1. ${90}^o$
2. ${105}^o$
3. ${110}^o$
4. None of these