The diagonals of a parallelogram:

The diagonals of a parallelogram:
  1. Are equal
  2. Bisect each other
  3. Are perpendicular
  4. Bisect the angles

Solution

Diagonals of any parallelogram bisect each other (each cuts the other into two equal halves), but in general they are neither equal nor perpendicular nor angle bisectors.

Asked in: IMO

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