a quadrilateral is a parallelogram if the diagonals bisect each other

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As per theorem 3 in quadrilaterals: A quadrilateral is a parallelogram if and only if the diagonals bisect each other. Hence , the statement is TRUE.

Answer:

  • If a quadrilateral has 2 sets of opposite angles congruent, then it is a parallelogram.
  • If a quadrilateral has consecutive angles which are supplementary, then it is a parallelogram.
  • If a quadrilateral has diagonals which bisect each other, then it is a parallelogram.

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