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Which property is NOT necessarily true for every parallelogram?

Class 8Understanding QuadrilateralsQuadrilaterals
  • ADiagonals are equal
  • BOpposite sides are equal
  • COpposite angles are equal
  • DDiagonals bisect each other

Step-by-Step Solution

Equal diagonals hold only for rectangles and squares. A general parallelogram has unequal diagonals, but always has equal opposite sides, equal opposite angles and bisecting diagonals.
Answer: A) Diagonals are equal

Key idea: Special parallelograms — extra properties

**Rectangle**: parallelogram + all angles 90°. Extra: diagonals are equal in length.

**Rhombus**: parallelogram + all sides equal. Extra: diagonals are perpendicular AND bisect the angles at each vertex.

**Square**: parallelogram + all angles 90° + all sides equal. Has both extras: equal AND perpendicular AND angle-bisecting diagonals.

Knowing the family tree saves you memorising overlapping rules — a square inherits everything from rectangle AND rhombus.

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