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McGraw Hill Integrated II, 2012 View details

3. Tests for Parallelograms

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Exercise 10 Page 500

What conditions must a quadrilateral satisfy to be a parallelogram?

Yes, 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.

We can see that only one pair of opposite sides are marked as parallel but we can also see that these two sides are congruent. Therefore, the last of the listed conditions is satisfied.