2. Properties of Parallelograms

5. Warm Up 3/17  Find the perimeter of triangle ABC: B 4 cm 3 cm 6 cm 2x cm x + 4 cm 4 cm A C

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

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

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

9. 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 

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

11. Example 1 FHGJ is a parallelogram. Find the unknown length. JG= JK=

12. Example 2  PQRS is a parallelogram. Find the angle measure. m  R = m  Q =

13. Example 3 ABCD is a parallelogram. Find x.

14. Example 4  Given the figure is a parallelogram find the value of x and y 84 o (3x+3) o 2y o

15. Example 5 ABCD is a parallelogram. The diagonals intersect at point E. Use the given information to solve for the variables m, n and x. CE = 3m AE = 15 A D C B E

16. Summarizer  Name 5 properties of parallelograms 1. opposite sides parallel 2. opposite sides congruent 3. opposite angles congruent 4. consecutive angles supplementary 5. diagonals bisect each other