1. 6-3: Tests for ParallelogramsW X Y Z
Today’s theorems are backwards (converses) from the ones from last lesson!!!
Theorem 6.9: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Example - in quadrilateral WXYZ, if  WYZ  YWX, how could you prove that WXYZ is a parallelogram?
Both pairs of opposite sides are congruent by CPCTC.

2. More theorems
Theorem 6.10: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6.11: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Theorem 6.12: If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.

3. Examples
Determine whether each quadrilateral is a parallelogram. If yes, give a reason. 1. 2.
1. yes, one pair of opp. sides both parallel and congruent
2. No only one pair of opp. Sides are congruent.

4. Example
Try Check your progress p #4A & 4B Find x and y so that the quadrilateral is a parallelogram.
4A: 56 = 7x, x = 8
5y – 26 = 4y + 4
y = 30
4B: x = 3, y = 7

5. Example
Try Check Your Progress page 336 #5: Determine whether the figure with the given vertices is a parallelogram. Use the midpoint formula to check if the diagonals bisect each other. The slope formula could also be used to determine if the opposite sides are parallel.
Graph
Answer: No

6. Try these
Page 337 #3-7
No, one pair of opp. Sides are not parallel and congruent.
Yes: each pair of opp. angles is congruent.
x = 13, y = 4
x = 41, y = 16
Yes
Homework #39: p , 20-27, 32, 36, 39, 40