1. Class Opener 1/5/12 Use the properties of a kite to determine the value of each variable and each side length
3x - 4 x
2y - 5
Y + 1

2. Properties of a Parallelogram
Opposite sides of a parallelogram are congruent.

3. Example
Find the value of x in PQRS
3x - 15 R Q P S
2x + 3

4. Properties of a Parallelogram
Opposite angles of a parallelogram are congruent.

5. 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
X + Y = 180 Y

6. Example
Find the value of Y in the following parallelogram. Then find all the angle measures. ?
3y +37 ?
6y + 4

7. Properties of a Parallelogram
The diagonals of a parallelogram bisect each other.

8. Example
Find the value of A and B A
B + 10
B+2
2A – 8

9. 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.

10. 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 H 2 C G 2 B F 2
2.5 A E