Notes Parallelograms-3301451_l_v2_05v_s1

Parallelograms

Dan Greenberg
Lori Jordan

Andrew Gloag
Victor Cifarelli
Jim Sconyers

Bill Zahner

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Printed: July 3, 2017

www.ck12.org Chapter 1. Parallelograms

1CHAPTER Parallelograms

Learning Objectives
Here you’ll learn what a parallelogram is and how apply theorems about its sides, angles, and diagonals to solve for
unknown values.

Parallelograms
A parallelogram is a quadrilateral with two pairs of parallel sides.

Notice that each pair of sides is marked parallel (for the last two shapes, remember that when two lines are
perpendicular to the same line then they are parallel). Parallelograms have a lot of interesting properties.
Facts about Parallelograms

1. Opposite Sides Theorem: If a quadrilateral is a parallelogram, then both pairs of opposite sides are congru-
ent.

If

then

2. Opposite Angles Theorem: If a quadrilateral is a parallelogram, then both pairs of opposite angles are
congruent.
If

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then

3. Consecutive Angles Theorem: If a quadrilateral is a parallelogram, then all pairs of consecutive angles are
supplementary.
If

then

m A + m D = 180◦
m A + m B = 180◦
m B + m C = 180◦
m C + m D = 180◦
4. Parallelogram Diagonals Theorem: If a quadrilateral is a parallelogram, then the diagonals bisect each other.
If

then
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Vocabulary

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