1. Properties of Parallelograms Objective: To use relationships among sides, angles, diagonals or transversals of parallelograms.

2. 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)

3. Practice The opposite sides of a parallelogram are Represented by 2x+10 and 5x-20. Find the length of the Parallelogram represented By 4x-1.

4. Use KMOQ to find m O. Q and O are consecutive angles of KMOQ, so they are supplementary. Definition of supplementary angles m 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

5. Find the value of x in ABCD. Then find m A. 2x + 15 = 135Add x to each side. 2x = 120Subtract 15 from each side. x = 60Divide each side by 2. x + 15 = 135 – xOpposite 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 = 180Substitute 75 for m B. 6-2

6. Using Algebra Find the value of y in EFGH. Then find m<E, m<F, m<G, m<H. EF G H 3y + 37 6y + 4

7. Example 3y-7 X+1y 2x