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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 69 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.

Looking at the congruence and parallel markings, we can only be certain that one pair of opposite sides is both parallel and congruent. Recall that for a quadrilateral to be a parallelogram, a pair of opposite sides must be both parallel and congruent. Therefore, it is a parallelogram.

Subchapter links

Lesson Check p.654

Practice and Problem-Solving Exercises p.654-657

Standardized Test Prep p.657

Mixed Review p.657