Properties of Rhombus

Q. ABCD is a rhombus with ∠ABC = 126°, find the measure of ∠ACD.

1. 27°
2. 63°
3. 90°
4. 153°

Q. In the given figure, ABCD is a rhombus. Find the values of x, y and z.

1. x = 13
   y = 6
   z = 2.5
2. x = 12
   y = 5
   z = 13
3. x = 13
   y = 12
   z = 5
4. x = 13
   y = 24
   z = 10

Q.

Construct a rhombus ABCD with AB = 4.5 cm and AC = 6 cm. [4 MARKS]

Q.

Construct a rhombus $ABCD,$ with $AC=6cm$ and $BD=4.6cm.$

Q.

If a diagonal of a quadrilateral bisect both the angles, then it is a

1. Kite

2. Parallelogram

3. Rhombus

4. Rectangle

Q.

Diagonals are equal in square and _______ .

1. Trapezium

2. Kite

3. Rhombus

4. Rectangle

Q. The quadrilateral which has the properties of both a parallelogram and a kite is .

1. rhombus
2. rectangle
3. square

Q.

The midpoints of the adjacent sides of a rhombus will form a rectangle. State whether the given statement is true or false.

1. True

2. False

Q. The following figure RUNS is a parallelogram.​
Find $x$ and $y$. (Lengths are in $cm$)

Q.

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

1. All sides of a rhombus are equal

2. Diagonals bisect each other

3. Diagonals bisect each other at right angles

4. Opposite angles are equal.

Q. ABCD is a rhombus with ∠ABC = 30°. The measure of ∠ACD (in degrees) is _____ .

1. 75

Q. The quadrilateral which has the properties of both a parallelogram and a kite is .

1. rhombus
2. rectangle
3. square

Q.

ABCD is a parallelogram and EFGB is a rhombus. AB = 7cm; AD = 4cm. If E is the mid-point of BC, find the perimeter of the whole figure i.e., ABGFECDA.

1. 24 cm

2. 30 cm

3. 26 cm

4. 28 cm

Q. If all the sides in a kite are equal, then it is called a ______.

1. rhombus
2. rectangle
3. trapezium
4. triangle

Q. In the given figure, ABCD is a rhombus. Find the values of x, y and z.

1. x = 12
   y = 5
   z = 13
2. x = 13
   y = 6
   z = 2.5
3. x = 13
   y = 12
   z = 5
4. x = 13
   y = 24
   z = 10

Q.

Construct a rhombus ABCD, with AC = 6 cm and BD = 4.6 cm. [4 MARKS]

Q. If all the interior angles of a rhombus are right angles, then it is a square.

1. False
2. True

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

1. All the sides of a rhombus are equal.
2. The angles of rhombus are right angles.
3. The adjacent angles of a rhombus are supplementary.
4. The diagonals of a rhombus bisect each other at right angles.

Q. ABCD is a rhombus with ∠ABC = 126°, find the measure of ∠ACD.

1. 27°
2. 63°
3. 90°
4. 153°

Q.

Select the correct statements.

1. True

2. False

3. All rhombuses are kites.
4. All parallelograms are kites