Properties of Parallelograms

Objective: To use relationships among sides, angles, diagonals or

transversals of parallelograms.

Summary of Properties

• Opposite sides are parallel• Opposite sides are equal• Opposite angles are equal• Consecutive angles are supplementary• diagonals bisect each other (cut each other in

half)

Practice

• The opposite sides of a parallelogram areRepresented by 2x+10 and5x-20. Find the length of theParallelogram represented By 4x-1.

Use KMOQ to find m O.

Q and O are consecutive angles of KMOQ, so they are supplementary.

Definition of supplementary anglesm O + m Q = 180

Substitute 35 for m Q.m O + 35 = 180

Subtract 35 from each side.m O = 145

Properties of Parallelograms

6-2

Find the value of x in ABCD. Then find m A.

2x + 15 = 135 Add x to each side.

2x = 120 Subtract 15 from each side.

x = 60 Divide each side by 2.

x + 15 = 135 – x Opposite angles of a are congruent.

Substitute 60 for x. m B = 60 + 15 = 75

Consecutive angles of a parallelogram are supplementary.

m A + m B = 180

Subtract 75 from each side.m A = 105

m A + 75 = 180 Substitute 75 for m B.

6-2

Using Algebra

• Find the value of y in EFGH. Then find m<E, m<F, m<G, m<H.

E F

GH

3y + 37

6y + 4

Example

3y-7

X+1 y

2x