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Which of the following quadrilaterals does NOT always have diagonals that bisect each other?

Class 9QuadrilateralsGeometry — Quadrilaterals
  • AParallelogram
  • BRectangle
  • CTrapezium
  • DRhombus

Step-by-Step Solution

Diagonals bisect each other in all parallelograms (including rectangles and rhombuses). A general trapezium is not a parallelogram, so its diagonals do not bisect each other.
Answer: C) Trapezium

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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