If a quadrilateral has both pairs of opposite sides equal AND its diagonals are perpendicular but unequal,…

If a quadrilateral has both pairs of opposite sides equal AND its diagonals are perpendicular but unequal, it is a:
  1. Rectangle
  2. Square
  3. Rhombus (but not a square)
  4. Trapezium

Solution

Opposite sides equal $\Rightarrow$ parallelogram. Perpendicular diagonals in a parallelogram $\Rightarrow$ rhombus. Unequal diagonals rule out the square.

Asked in: IMO

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