Construction of a Rhombus When One Side and One Angle Are Given.

Q.

Draw a rhombus whose side is 7.2 cm and one angle is ${60}^{\circ }$.

Q.

Let $ABCD$ be the parallelogram whose sides $\overrightarrow{AB}$and $\overrightarrow{AD}$ are represented by the vectors $2\hat{i}+4\hat{j}-5\hat{k}$ and $\hat{i}+2\hat{j}+3\hat{k}$ respectively. Then, if $\overrightarrow{a}$ is a unit vector parallel to $\overrightarrow{AC}$, then $\overrightarrow{a}$ is equal to ?

1. $\frac{3\hat{i}-6\hat{j}-2\hat{k}}{3}$

2. $\frac{3\hat{i}+6\hat{j}+2\hat{k}}{3}$

3. $\frac{3\hat{i}-6\hat{j}-2\hat{k}}{7}$

4. $\frac{3\hat{i}+6\hat{j}-2\hat{k}}{7}$

Q.

To construct a rhombus ABCD given AB=4 cm and $\angle ABC={120}^{\circ }$, which of the following properties of rhombus do we use?

1. Diagonals bisect each other.

2. Diagonals bisect each other at right angles.

3. All sides of rhombus are equal.

4. Opposite angles are equal.

Q. In the following parallelogram, find the value of $x$.

1. 11°
2. 22°
3. 33°
4. 44°

Q. Construct a rhombus ABCD, given it's diagonal AC = 6.3 cm and diagonal BD = 5.8 cm.

Q. Construct a rhombus with side of length $5cm$ and an acute angle of ${45}^{\circ }$. The area of the rhombus is: (approx.)

1. $14.2c{m}^2$
2. $17.5c{m}^2$
3. $35c{m}^2$
4. $30.9c{m}^2$

Q.

To construct a rhombus ABCD given AB=4 cm and $\angle ABC={120}^{\circ }$, which of the following properties of rhombus do we use?

1. All sides of rhombus are equal.

2. Diagonals bisect each other.

3. Diagonals bisect each other at right angles.

4. Opposite angles are equal.

Q. Draw rhombus KLMN such that its side is $4$ cm and $\angle K={75}^o$.

Q. Construct a rhombus with side of length $5cm$ and an acute angle of ${45}^{\circ }$. The length of the longer diagonal of the rhombus is:

1. $3.8cm$
2. $9.2cm$
3. $6.3cm$
4. $10.6cm$

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. Construct a rectangle ABCD, when:

Q. Construct a rhombus, having given one side = 4.8 cm and one angle = ${75}^{\circ }$.

Q. Construct a rhombus ABCD, given it's one side = 6 cm and $\angle A={60}^{\circ }$

Q. Construct a rhombus $ABCD$ whose length of one side $AB$ is $5cm$ and $\angle DAB=\frac{\pi }{2}$. Find the difference between the length of its diagonals.

Q. Draw the diagonals of the parallelogram. Then the sum of the lengths of the diagonals (in $cm$) is:
(Round off to the nearest integer)

Q. Construct a rhombus with side $4$ cm and one of its angles equal to ${45}^o$.

Q. Construct a rectangle ABCD, when:

Q. The perpendicular distances between the pair of opposite sides of a parallelogram are $3$ cm and $4$ cm, and one of its angles measures ${60}^{\circ }$. Using ruler and compasses only, construct the parallelogram.

Q.

Which property of a rhombus do we use to construct a rhombus given one side and one angle?

1. Sides of a rhombus are equal
   

2. Opposite angles are equal
   

3. Diagonals bisect each other
   

4. Diagonals bisect each other at right angles

Q. It is possible to construct a rhombus if only the length of its diagonals are known.

1. False
2. True

Q. Construct a rhombus $ABCD$ of side $4.6cm$ and $\angle BCD={135}^o$, by using ruler and compasses only.

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 188
Construct a rhombus whose side is 5 cm and one angle is of ${60}^{\circ }$.

Q. Construct a rhombus $ABCD,$ such that :
Base $AB=3.8cm$ and $\angle DAB={30}^o$

Q. Construct a rhombus $MATH$ with $AT=4cm,\angle MAT={120}^o$.