Rhombus

Q.

Can a rectangle be a rhombus?

Q.

Construct Rhombus $BEND$ with $BN=5.6cm$, $DE=6.5cm$.

Q.

Which quadrilaterals have diagonals that bisect each other?

Q. ABCD is a rectangle and P, Q, R, S are mid-points of the sides AB, BC, CD and DA respectively. The quadrilateral PQRS is a rhombus.

1. True
2. False

Q.

$\mathrm{ABCD}$ is a rhombus such that $\angle \mathrm{ACB}=40°$ Then $\angle \mathrm{ADB}$ is

1. $40º$

2. $45º$

3. $50º$

4. $60º$

Q. A quadrilateral whose adjacent sides are equal is called a .

1. Kite
2. Rectangle
3. Trapezium
4. Parallelogram

Q.

Every rhombus will have two acute angles and two obtuse angles.

1. True

2. False

Q.

In the figure ABCD is a rhombus. If ∠A =70^o, then ∠CDB is

1. 50^o

2. 40^o

3. 55^o

4. 60^o

Q.

A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

Q. $\text{In given figure, ABCD is a rhombus.}\text{If}\angle OAB={40}^{\circ },\text{then find the value of x.}$

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${50}^{\circ }$
4. ${55}^{\circ }$

Q.

We get a rhombus by joining the mid-points of the sides of a

1. parallelogram

2. rhombus

3. rectangle

4. triangle

Q. Question 12
E and F are respectively the mid-points of the non-parallel sides AD and BC of a trapezium ABCD, Prove that $EF||ABandEF=\frac{1}{2}(AB+CD)$.

Q. In the given figure, ABCD is a rhombus, then the value of x - y is

1. ${50}^{\circ }$
2. ${40}^{\circ }$
3. ${30}^{\circ }$
4. ${20}^{\circ }$

Q. If ABCD is a rhombus, then which of the following is true?

1. $AB=BC=CD=DA$
2. $AB=\frac{BC}{2}=CD=\frac{DA}{2}$
3. $AB=2BC=3CD=4DA$
4. $AB=BC=2CD=2DA$

Q. ABCD is a rhombus if $\angle A={65}^{\circ }$, find $\angle CDB$.

1. ${37}^{\circ }$
2. ${57.5}^{\circ }$
3. ${55.5}^{\circ }$
4. ${75}^{\circ }$

Q.

A rhombus is symmetrical about its __________________

Q. In the given figure, if ABCD is a rhombus with $\angle ADC=58°$, then the measure of 2$\angle CAB–\angle ABD$ is equal to

1. ${30}^0$
2. ${25}^0$
3. ${38}^0$
4. ${93}^0$

Q.

If the diagonal BD of a parallelogram bisects $\angle$B and $\angle$D, then ABCD is a

1. Rectangle

2. Rhombus

3. Square

4. Trapezium

Q. Diagonals of a rhombus intersect at an angle of _____ .

1. ${90}^{\circ }$
2. ${45}^{\circ }$
3. ${30}^{\circ }$
4. ${60}^{\circ }$

Q.

In the given figure, ABCD is a rhombus. If OB = 3 units, OC = 4 units and AE = 6.4 units. Find the length of BE.

1. 0.8 units

2. 0.4 units

3. 1.4 units

4. 1.6 units

Q. In the figure given below,
ABCD is a rhombus. Find the value of x.

1. ${20}^{\circ }$
2. ${25}^{\circ }$
3. ${30}^{\circ }$
4. ${50}^{\circ }$

Q.

The diagonals of a rhombus are perpendicular to each other.

1. True
2. False

Q. Prove that the figure formed by joining the mid points of the adjacent sides of a rectangle is a rhombus.

Q. If two consecutive sides of a rhombus are represented by $(5x+10)$ and $(3x+14)$, then the perimeter of the rhombus is

1. 24 units
2. 80 units
3. 60 units
4. 40 units

Q.

Is quadrilateral ABCD a rhombus?

I. Quadrilateral ABCD is a ||gm.

II. Diagonals AC and BD are perpendicular to each other.

The correct answer is: (a)/(b)/(c)/(d).

Q. Question 4
ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus.

Q. In the given figure, $ABCD$ is a rhombus. Diagonals $AC$ and $BD$ intersect at $O$. $E$ and $F$ are mid points of $AO$ and $BO$ respectively. If $AC=16cm$ and $BD=12cm$, then $EF$ is:

Q.

In the given figure, AP $\parallel$ BQ $\parallel$ CR. Prove that ar ($△$AQC) = ar ($△$PBR).
[2 MARKS]

Q. Question 10
Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order. [Hint: Area of a rhombus = $\frac{1}{2}$(product of its diagonals)]

Q.

A parallelogram whose all sides are equal is called a _____.

1. trapezium

2. rhombus

3. rectangle

4. kite