Class Opener 1/5/12

Use the properties of a kite to determine the value of each variable and each side length

2y - 5 Y +

1

3x - 4

x

Properties of a Parallelogram

• Opposite sides of a parallelogram are congruent.

Example

• Find the value of x in PQRS

P S

RQ3x - 15

2x + 3

Properties of a Parallelogram

• Opposite angles of a parallelogram are congruent.

Angles inside a Parallelogram

• The angles inside any polygon that share a side are known as Consecutive Angles. A parallelogram has opposite sides parallel. Its consecutive angles are same side interior angles that add up to 180 degrees.

X

Y

X + Y = 180

Example

• Find the value of Y in the following parallelogram. Then find all the angle measures.

3y +37

6y + 4 ?

?

Properties of a Parallelogram

• The diagonals of a parallelogram bisect each other.

Example

• Find the value of A and B

AB + 10

2A – 8 B+2

Properties of Parallelograms

• If 3 or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

Example

• In the figure to the right, DH CG BF and AE are parallel. AB = BC = CD = 2, and EF = 2.5. Find EH

D

C

B

A

2

2.52

2

E

H

G

F