Diagonals of a Rhombus Are Perpendicular to Each Other

Q. ABCD is rhombus. If the length of AC and BD are 8 cm and 6 cm respectively, then find the length of the sides.

1. 3 cm
2. 5 cm
3. 6 cm
4. 4 cm

Q. Diagonals of a parallelogram intersect each other at point O. If AO = 5, BO = 12 and AB = 13 then show that $\square$ABCD 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. ${55}^{\circ }$
2. ${30}^{\circ }$
3. ${50}^{\circ }$
4. ${45}^{\circ }$

Q.

In the given figure, ABCD is a rhombus in which diagonals AC and BD intersect at O. Then measure of ∠AOB is.

1. 45^o

2. 60^o

3. 80^o

4. 90^o

Q.

Which of these is a condition for a parallelogram to be a square?

1. Diagonals are equal and perpendicular

2. Diagonals are angle bisectors

3. Opposite angle should not be equal

4. One side should not be parallel to another

Q.

The perimeter of a square is 4x + 20 cm. Then find the length of diagonal

Q. If one of the diagonals of square is 8 cm, then the length of the other diagonal is .

1. 4 cm
2. 8 cm
3. 6 cm
4. 5 cm

Q. In the given rhombus ABCD, If the length of diagonals of rhombus are 8 cm and 6 cm, then the side of the rhombus is .

1. 3 cm
2. 6 cm
3. 4 cm
4. 5 cm

Q. P and Q are any two points lying on the sides DC and AD respectively of a square ABCD.
Show that ar(APB) = ar(BQC).

Q. The lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively. Find the length of each side of the rhombus.

Q.

Which of the following quadrilateral is not a rhombus?

1. Diagonals bisect opposite angles

2. All four sides are equal

3. Diagonals bisect each other

4. One angle between the diagonals is 60°

Q. Three statements are given below:
I. In a rectangle ABCD, the diagonal AC bisects ∠A as well as ∠C.
II. In a square ABCD, the diagonal AC bisects ∠A as well as ∠C.
III. In a rhombus ABCD, the diagonal AC bisects ∠A as well as ∠C.
(a) I only
(b) II and III
(c) I and III
(d) I and II

Q. Diagonals of a rhombus are to each other.

1. equal
2. perpendicular
3. parallel

Q. Square ABPQ and ADRS are drawn on the sides AB and AD of a parallelogram ABCD. Which of the following options is correct?

1. $\angle SAQ=\angle ABC$
2. $\angle SRD=\angle ADC$
3. $\angle SAD=\angle ABC$
4. $\angle SAQ=\angle DAB$

Q. A quadrilateral with all four sides equal, each angle not equal to 90° is , and diagonals of such a quadrilateral intersect at
.

1. rhombus
2. 45°
3. kite
4. 90°

Q. The perimeter of a rhombus is $96$ cm and obtuse angle of it is ${120}^o$. Find the lengths of its diagonals.

1. $12\text{cm},12\sqrt{3}\text{cm}$
2. $18\text{cm},18\sqrt{3}\text{cm}$
3. $24\text{cm},24\sqrt{3}\text{cm}$
4. $32\text{cm},32\sqrt{3}\text{cm}$

Q. ABCD is a rectangle in which diagonal BD bisects ∠B. Show that ABCD is a square.

Q. ABCD is rhombus. If the length of AC and BD are 8 cm and 6 cm respectively, then find the length of the sides.

1. 3 cm
2. 4 cm
3. 5 cm
4. 6 cm

Q. In rhombus $ABCD,A{B}^2+B{C}^2+C{D}^2+D{A}^2=$ _____ .

1. $O{C}^2+O{B}^2$
2. $O{A}^2+O{B}^2$
3. $O{B}^2+O{C}^2$
4. $A{C}^2+B{D}^2$

Q. Which of the following quadrilateral has equal diagonals?

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

Q. P and Q are any two points lying on the sides DC and AD respectively of a square ABCD.
Show that ar(APB) = ar(BQC).

Q. The lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively. Find the length of each side of the rhombus.

Q. Which of the following is not the property of a rhombus?

1. Diagonals are equal
2. All sides are equal
3. Diagonals bisect each other
4. Opposite angles are equal

Q. If D and E are the mid-points of AB and AC of ΔABC respectively, then which of the following are not true?

1. DE $\parallel$ BC
2. 2 × DE = BC
3. DE = $\frac{1}{2}$ × BC
4. DE = 2 × BC

Q. In the given rhombus ABCD, If the length of diagonals of rhombus are 8 cm and 6 cm, then the side of the rhombus is .

1. 3 cm
2. 6 cm
3. 4 cm
4. 5 cm

Q.

ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that:

(i) ABCD is a square (ii) diagonal BD bisects ∠B as well as ∠D.

Q.

Which of the following is/are true about the diagonals of a rhombus?

1. Diagonals are equal in length.

2. Diagonals are perpendicular to each other.

3. Diagonals are bisectors of each other.

4. Only one of the diagonals bisect the other.

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. At what angle do the diagonals of a rhombus bisect each other?

1. 90 degrees
2. 180 degrees
3. 80 degrees
4. 0 degrees

Q. A quadrilateral with all four sides equal, each angle not equal to 90° is , and diagonals of such a quadrilateral intersect at
.

1. rhombus
2. 45°
3. kite
4. 90°