Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
6. Circles and Arcs
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Exercise 68 Page 657

What conditions must a quadrilateral satisfy to be a parallelogram?

Is the Figure a Parallelogram? Yes
Explanation: See solution.

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.

By looking at the diagonals, we can see both diagonals bisect each other. Recall that for a quadrilateral to be a parallelogram, both diagonals must be bisected. Therefore, it is a parallelogram.