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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 14 Page 418

What conditions must a quadrilateral satisfy to be a parallelogram?

No.

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.

For the quadrilateral to be a parallelogram, both pairs of opposite angles must be congruent. In our case we do not know if they are congruent. Therefore, it is not necessarily 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