OBJECTIVES: 1) TO USE RELATIONSHIPS AMONG SIDES AND AMONG ANGLES OF PARALLELOGRAMS. 2) TO USE RELATIONSHIPS INVOLVING DIAGONALS OF PARALLELOGRAMS OR TRANSVERSALS. 6-2 Properties of Parallelograms M11.C C

Theorem Opposite sides of a parallelogram are congruent. Symbol

Example Draw parallelogram PQRS. Find x. QR = 3x – 15 PS = 2x + 3

Vocabulary Consecutive Angles – Angles of a polygon that share a side. They are equal to 180.

Examples: Using Consecutive Angles Find m ∠O.

Theorem Opposite angles of a parallelogram are congruent

Example: Use opposite angles Find the value of x in quadrilateral ABCD. Then find the m ∠A

Theorem The diagonals of a parallelogram bisect each other.

Example: Using Diagonals Parallelogram ABCD Diagonals meet at E AE= 3y - 4 EC=y BE= x + 15 ED= 6x Find x and y. Find AE, EC, BE, and ED.

Classwork HANDED-IN Pg 297 #1-14 Page 297 #15, 16, Bonus #48