2. Properties of Parallelograms

3. Definition  Parallelogram – a quadrilateral with both pairs of opposite sides parallel.

4. Theorem: Opposite Sides  If a quadrilateral is a parallelogram, then its opposite sides are congruent. and

5. Theorem: Opposite Angles  If a quadrilateral is a parallelogram, then its opposite angles are congruent.  P   R and  Q   S

6. Theorem: Consecutive Angles  If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. m  P + m  Q = 180 , m  Q + m  R = 180 , m  R + m  S = 180 , m  S + m  P = 180 

7. Theorem: Bisecting Diagonals  If a quadrilateral is a parallelogram, then its diagonals bisect each other. and

8. Example 1 FHGJ is a parallelogram. Find the unknown length. JG= JK= JG = FH (opposite sides of a parallelogram are  ) JG = 5 JK = HK (diagonals of a parallelogram bisect each other) JK = 3

9. Example 2  PQRS is a parallelogram. Find the angle measure. m  R = m  Q = m  R = 65  (opp. angles of a parallelogram are  ) m  Q = 180 - 65  (consecutive angles are supp.) m  Q = 115 

10. Example 3 ABCD is a parallelogram. Find x. 3x + 120 = 180 3x = 60 x = 20

11. Homework  Page 306-307 Numbers 1 – 19 all