6.2 Properties of Parallelograms

Objective: - Use some properties of parallelograms

Polygons

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Notice the matching arrowheads to show the parallel sides.

Theorem

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Theorem

If a quadrilateral is a parallelogram, then its opposite angles are congruent.

Theorem

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

Theorem

If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Using Properties of Parallelograms

How long are JK and JH? JK = 3Diagonals of a bisect each other. JH = 5Opposite sides of a are

F G

JH

5

3K

Using Properties of Parallelograms

What is the measure of angle F?110˚What is the measure of Angle J?70˚

F G

JH

70˚

Using Properties of Parallelograms

What is x?3x + 120 = 1803x = 60x = 20

F G

JH

120˚ 3x

Using Facts about Parallelograms in a Proof

Look at Example 4 on p. 332.Look at Example 5 on p. 332.Look at Example 6 on p. 333.Do p. 333 1-19, 47-49

F G

JH

Homework:

worksheets