Construction of Parallelogram When Both the Diagonals and the Angle between Them Are Given Are Given.

Q.

To construct a parallelogram whose one side and two diagonals are given, which property of the parallelogram do we use?

1. Opposite sides are equal.

2. Diagonals bisect each other.

3. Diagonals bisect each other at ${90}^{\circ }$.

4. Opposite angles are equal.

Q. Question 130
State whether the statements are True or False.
A parallelogram can be constructed uniquely, if both diagonals and the angle between them is given.

Q.

To construct a parallelogram given its length of diagonals, which of the following additional information is required?

1. One angle of the parallelogram

2. Two angles of the parallelogram

3. The angle between the diagonals

4. None of the above

Q. Draw a parallelogram ABCD. such that l(DC) = 5.5 cm, m∠D = 45^ᴏ, l(AD) = 4 cm.

Q.

Parallelogram with one side 5 centimetres; diagonals 8 centimetres and 6 centimetres.

Q.

At least 2 rays need to be constructed to divide a line segment in a given ratio

1. True

2. False

Q. Construct the parallelograms with the given measurements and find their area.
ARTS, AR = 6 cm, RT = 5 cm and ∠ART = 70°.
$\left[5\right]$

Q. The acute angle made by the sides of the parallelogram is:

1. ${60}^{\circ }$
2. ${55}^{\circ }$
3. ${50}^{\circ }$
4. ${45}^{\circ }$

Q. George wanted to construct a parallelogram ABCD with sides AB = 5 cm, BC = 4 cm, CD = 5 cm, $\angle B={40}^{\circ }$ and $\angle C={120}^{\circ }$. He can construct a parallelogram with the following measure requirement provided . State whether the statement is True or False .

1. Yes, of course

2. With ADC, yes

Q.

Parallelogram with adjacent sides 6.5 centimetres and 4 centimetres, angle between them 45°.

Q. Construct a trapezium ABCD where AB is parallel to CD, AD = BC = 2 cm, AB = 10 cm and CD = 12 cm

Q. Construct a parallelogram $ABCD$, in which diagonal $AC=3.8cm$, diagonal $BD=4.6cm$ and the angle between $AC$ and $BD$ is ${60}^{\circ }$.

Q. Construct a parallelogram $ABCD$, when diagonal $AC=6.4cm$, diagonal $BD=8.2cm$ and angle between the diagonals $={60}^{\circ }$. Then the perimeter of the parallelogram (in $cm$) is:

Q.

Construct a parallelogram ABCD in which AB = 6.5 cm, AC = 3.4 cm and the altitude AL from A is 2.5 cm. Draw the altitude from C and measure it.

Q. Using ruler and compasses only, draw a parallelogram whose diagonals are $4cm$ and $6cm$ long and contain an angle of ${75}^o$. Measure and write down the length of one of the shorter sides of the parallelogram.

Q. Draw parallelogram ABCD with AC = 9 cm, BD = 7 cm and $\angle$ AOB = ${120}^o$ where $\overline{AC}$ and $\overline{BD}$ intersect at O and find its area.

Q. In a parallelogram diagonals each other.

1. trisect
2. bisect
3. Perpendicular to

Q.

Construct a parallelogram ABCD, in which diagonal AC = 3.8 cm, diagonal BD = 4.6 cm and the angle between AC and BD is ${60}^{\circ }$

Q. Draw a seg PQ of length 9 cm and divide it in the ratio 3 : 2.

Q. Write the steps of construction of a parallelogram $ABCD$ in which diagonal $AC=6.3cm$; diagonal $BD=7cm$ and the acute angles between the diagonals is ${45}^{\circ }$.

Q.

Construct a parallelogram ABCD such that AC = 6 cm, BD = 4.6 cm and angle between them is ${45}^{\cdot }$

Q. Construct a parallelogram whose diagonal are $8.4$ cm and $10.6$ cm and an angle between them is ${50}^o$.

Q. Use ruler and compasses to construct a parallelogram with diagonals 6 cm and 8 cm in length having given the acute angle between them is ${60}^{\circ }$.

Q. Construct a parallelogram $ABCD$, where $AB=7cm,AC=9cm$ and $\angle A={75}^{\circ }$.