6.2 Properties of Parallelograms

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

• In a quadrilateral, opposite sides do not share a vertex and opposite angles do not share a side.

Theorem 6.3

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

Consecutive Angles

• Angles of a polygon that share a side are consecutive angles.

Theorem 6.4

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

Using Consecutive Angles

• What is the measure of angle P in parallelogram PQRS?

A. 26°B. 64°C. 116°D. 126°

180m P m S

64 180m P

116m P

Theorem 6.5

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

Theorem 6.6

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

Using Algebra to Find Lengths

• Solve a system of linear equations to find the values of x and y in parallelogram KLMN. What are KM and LN?

Using Algebra to Find LengthsKP MP

LP NP10 2 8y x

2x y 10 2( 2) 8y y 10 2 4 8y y 10 4y 14 y14 2x 16x

2( )KM KP2( 10)KM y 2(14 10) 48

2( )LN LP2LN x2(16)32

Theorem 6.7

• If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

Using Parallel Lines and Transversals

• In the figure, AE || BF || CG || DH, AB = BC = CD = 2, and EF = 2.25. What is EH?

EF = FG = GH

EH = EF + FG + GH

EH = 2.25 + 2.25 + 2.25

EH = 6.75

More Practice!!!!!

• Homework – p. 364 - 365 #9 – 12, 14 – 27, 29 – 30 ALL.