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McGraw Hill Glencoe Geometry, 2012

MH

McGraw Hill Glencoe Geometry, 2012 View details

3. Tests for Parallelograms

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Exercise 13 Page 418

What conditions must a quadrilateral satisfy to be a parallelogram?

Yes.

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 markings, we can see that both diagonals are bisecting each other. Therefore, it is a parallelogram.

Subchapter links

Check Your Understanding p.417-418

H.O.T. Problems p.420

Standardized Test Practice p.421

Spiral Review p.421

Skills Review p.421