6-2 Parallelograms

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

Recall: Properties for parallel lines x 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.

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.

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

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

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

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

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

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

Homework Pg. 407-408 #8-20 all #8 is a T-Chart Proof!!! Look at the Elmo for Clues!