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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 1 Page 499

What conditions must a quadrilateral satisfy to be a parallelogram?

Yes; each pair of opposite angles are congruent.

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.

Looking at the angle markings, we can see that both pairs of opposite angles are congruent. Therefore, it is a parallelogram.

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