Which statement correctly describes the diagonals of a square?

Class 9QuadrilateralsGeometry — Quadrilaterals

AThey are equal, bisect each other, and are perpendicular
BThey are equal and bisect each other, but are not perpendicular
CThey bisect each other at right angles, but are not equal
DThey are perpendicular but do not bisect each other

Step-by-Step Solution

A square is both a rectangle (equal diagonals) and a rhombus (perpendicular diagonals), so its diagonals are equal, bisect each other, and are perpendicular.

Answer: A) They are equal, bisect each other, and are perpendicular

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.

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