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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 11 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.

One pair of opposite sides is congruent. However, for it to be parallelogram, both pairs of opposite sides must be congruent. Therefore, it is not necessarily a parallelogram.

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