Properties of Parallelograms

1. Properties of Parallelograms

2. Definition • Parallelogram – a quadrilateral with both pairs of opposite sides parallel.

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

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

5. 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

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

7. 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

8. 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

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

10. Summarizer • Name 5 properties of parallelograms • opposite sides parallel • opposite sides congruent • opposite angles congruent • consecutive angles supplementary • diagonals bisect each other