1. 6.3 Conditions for Parallelograms

2. Conditions for Parallelograms
The figure is a parallelogram if…
Both pairs of opposite sides are congruent
Both pairs of opposite angles are congruent
Consecutive angles are supplementary
Diagonals bisect each other
One pair of opposite sides are both parallel and congruent

3. Examples
1) Show that JKLM is a parallelogram for a = 3 and b = 9.

4. Examples:
2) Show that PQRS is a parallelogram for x = 10 and y = 6.5.

5. Example
3) Show that PQRS is a parallelogram for a = 2.4 and b = 9.

6. Example
4) Determine if the quadrilateral must be a parallelogram. Justify your answer.

7. Example
5) Determine if the quadrilateral must be a parallelogram. Justify your answer.

8. Example
6) Determine if the quadrilateral must be a parallelogram. Justify your answer.

9. Example
7) Determine if each quadrilateral must be a parallelogram. Justify your answer.

10. Example
8) Determine if the set of vertices below form a parallelogram. J(–1, –6), K(–4, –1), L(4, 5), M(7, 0).

11. Example Determine if the set of vertices below form a parallelogram.
(1, 1) (6, 3) (8, -2) (3, -4)

12. Example Determine if the set o vertices below form a parallelogram.
(-5, -1) (0, 9) (11, 11) (5, 1)