1. 6-2 Parallelograms

2. Parallelogram
A quadrilateral where both pairs of opposite sides are parallel.

3. Recall: Properties for parallel linesx z y
Recall: Properties for parallel lines
x and y are CIA angles
Therefore, x and y are supplements
x + y = 180
x and z are also CIA therefore also supplements
x + z = 180
So, y = z
Supps of the same angle are congruent.

4. x
Theorem y
Opposite angles of a parallelogram are congruent. (x and Y are “opposite angles”)
Opposite sides of a parallelogram are congruent.
Diagonals of a parallelogram bisect each other.

5. Example Given: BC = 8, AB = 15, EC = 8, DB = 18. Find: AD DC 8 AE ACDE 8 A 15 B 15 8 E 8 16 8 18 9 C D 9

6. Example
Given: Angle ADC = 82, Angle EDC = 26
Find angles:
ADE
ABC
EBC
BCD
BEC A 56 B 82 82 9 56 E 56 56 8 98 56 8 82 98 56 26 C D

7. TOO If ABCD is a parallelogram, what is the length of segment BD?7 6 5

8. TOO
Solve for x, y and z 12
130 10 x y z

9. s = 3 A.) If WXYZ is a parallelogram, find the value of r.
B. If WXYZ is a parallelogram, find the value of s.
8s = 7s + 3
s = 3

10. C. If WXYZ is a parallelogram, find the value of t.
mYWX =mWYZ Alt. Int. Angles
2t = 18
t = 9

11. Homework
Pg #8-20 all
#8 is a T-Chart Proof!!! Look at the Elmo for Clues!