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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
3. Tests for Parallelograms
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Exercise 14 Page 500

What conditions must a quadrilateral satisfy to be a parallelogram?

No.

Practice makes perfect

To prove that a quadrilateral is a parallelogram, it is enough to show that one of the following conditions is satisfied.

  • Both pairs of opposite sides are parallel.
  • Both pairs of opposite sides are congruent.
  • Both pairs of opposite angles are congruent.
  • The diagonals bisect each other.
  • A pair of opposite sides is both parallel and congruent.

Let's analyze the given quadrilateral.

For the quadrilateral to be a parallelogram, both pairs of opposite angles must be congruent. In our case we do not know if they are congruent. Therefore, it is not necessarily a parallelogram.

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