Assertion (A): The diagonals of a rhombus are equal. Reason (R): A rhombus is a parallelogram with all sides equal. Which is correct?

Class 9QuadrilateralsGeometry — Quadrilaterals

ABoth A and R are true and R explains A
BBoth A and R are true but R does not explain A
CA is false but R is true
DBoth A and R are false

Step-by-Step Solution

The diagonals of a rhombus are perpendicular but NOT equal (unless it is a square), so A is false. R is a correct definition of a rhombus, so R is true.

Answer: C) A is false but R is true

Key idea: Special parallelograms

**Rectangle** (parallelogram + all angles 90°):
- All properties of a parallelogram.
- Diagonals are EQUAL (in addition to bisecting each other).

**Rhombus** (parallelogram + all sides equal):
- All properties of a parallelogram.
- Diagonals bisect each other AT RIGHT ANGLES.
- Diagonals also bisect the angles of the rhombus.

**Square** (rectangle + rhombus):
- All properties of both.
- Diagonals: equal, bisect at right angles, AND bisect angles.

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Quadrilaterals practice questions

More Class 9 Quadrilaterals practice

If one angle of a parallelogram is a right angle, then the parallelogram must be a ____.In ΔABC, the mid-point of BC is M and the mid-point of AC is N. If MN = 3.5 cm, what is…Which of the following quadrilaterals does NOT always have diagonals that bisect each…The sum of all the EXTERIOR angles of any quadrilateral (one at each vertex) is ____…The diagonals of a rhombus are 24 cm and 10 cm. Find the side of the rhombus (in cm).