Diagonals of a Rhombus are Perpendicular to Each Other

Q.

Name the quadrilaterals whose diagonals are perpendicular bisectors of each other.

Q.

Any parallelogram in which the diagonals are perpendicular bisectors of each other will be a square.

1. False

2. True

Q.

The angle bisectors of a rectangle will form a

1. rhombus

2. Square

3. Hexagon

4. rectangle

Q. Diagonals of a rhombus are 20 cm and 21 cm respectively, then find the side of rhombus and its perimeter.

Q. In a rhombus PQRS if PQ = 7.5 cm then find the length of QR. If $\angle QPS={75}^{\circ }$ then find the measure of $\angle PQR\text{and}\angle SRQ.$

Q. In the above figure, ABCD is a rhombus and CDEF is a square. if ∠ABC = 56${}^{\circ }$ , find: ∠DAG.

1. 47${}^{\circ }$
2. 17${}^{\circ }$
3. 27${}^{\circ }$
4. 37${}^{\circ }$

Q. ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.
$\left[2Marks\right]$

Q. ABCD is a rhombus with diagonals AC and BD.
$\text{The value of}p+q+r+s+t\text{is}$ .

1. ${270}^{\circ }$
2. ${180}^{\circ }$
3. ${360}^{\circ }$
4. ${540}^{\circ }$

Q. ABCD is a rhombus with diagonals AC and BD.
$\text{The value of}p+q+r+s+t\text{is}$ . (3 marks)

Q.

If the angles of a rhombus are made equal then it is a square. Sate True/False.

1. True

2. False

Q. ABCD is a rhombus with diagonals AC and BD.
$\text{The value of}p+q+r+s+t\text{is}$ .

1. ${540}^{\circ }$
2. ${180}^{\circ }$
3. ${360}^{\circ }$
4. ${270}^{\circ }$

Q.

Statement 1: Diagonals of a rhombus intersect at right angles.

Statement 2: All sides of a rhombus are equal.

Choose the correct statement.

1. Statement 1 is true, statement 2 is false

2. Statement 1 and statement 2, both are true

3. Statement 1 and statement 2, both are false

4. Statement 1 is false, statement 2 is true

Q. Is a square a special type of rhombus? I think that clearly square is a special type of rhombus as it is just a rhombus with angle measuring 90 degrees. But my teacher said that this is wrong because diagonals of rhombus are unequal and diagonals of a square equal. Thus, it is wrong, square can't be called a rhombus. Please clarify.

Q. ABCD is a rhombus with diagonals AC and BD.
$\text{The value of}p+q+r+s+t\text{is}$ .

1. ${270}^{\circ }$
2. ${180}^{\circ }$
3. ${540}^{\circ }$
4. ${360}^{\circ }$

Q. ABCD is a rhombus with diagonals AC and BD.
$\text{The value of}p+q+r+s+t\text{is}$ .

1. ${270}^{\circ }$
2. ${180}^{\circ }$
3. ${360}^{\circ }$
4. ${540}^{\circ }$

Q. Which of the following is not a parallelogram?

1. Square
2. Rectangle
3. Rhombus
4. Kite

Q. ___ is a quadrilateral whose diagonals are not equal but bisect each other at right angle.

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