1. Warm Up 6.3 on desk
Do daily Quiz 6.2

2. 6.3 Essential Objective: Essential Question:
Show that a quadrilateral is a parallelogram.
Essential Question:
How do we prove that a quadrilateral is a parallelogram?

3. Theorem 6.6
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

4. Tell whether the quadrilateral is
Example 1
Use Opposite Sides
Tell whether the quadrilateral is
a parallelogram. Explain your reasoning.
SOLUTION
The quadrilateral is
not a parallelogram.

5. Example 2
Use Opposite Angles
Tell whether the quadrilateral is a parallelogram. Explain your reasoning.
SOLUTION
The quadrilateral
is a parallelogram

6. Checkpoint
Use Opposite Sides and Opposite Angles
In Exercises 1 and 2, tell whether the quadrilateral is a parallelogram. Explain your reasoning. 1. 2.

7. Opposite sides are congruent.
Checkpoint
Use Opposite Sides and Opposite Angles
In Exercises 1 and 2, tell whether the quadrilateral is a parallelogram. Explain your reasoning. 1.
ANSWER
Yes; both pairs of
Opposite sides are congruent. 2.
No; opposite angles
Are not congruent.
ANSWER 7

8. Theorem 6.8
If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.

9. Example 3
Use Consecutive Angles
Tell whether the quadrilateral is a parallelogram. Explain your reasoning. a. b. c. 9

10. Theorem 6.9
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

11. Example 4
Use Diagonals
Tell whether the quadrilateral is a parallelogram. Explain your reasoning. a. b. 11

12. No; opposite angles are not congruent (or consecutive angles are
Checkpoint
Use Consecutive Angles and Diagonals
Tell whether the quadrilateral is a parallelogram. Explain your reasoning. c.
ANSWER
No; opposite angles are
not congruent (or
consecutive angles are
not supplementary). d.
Yes; one angle is
supplementary to both of
its consecutive angles.
ANSWER 12

13. Yes; the diagonals bisect each other.
Checkpoint
Use Consecutive Angles and Diagonals
Tell whether the quadrilateral is a parallelogram. Explain your reasoning. e.
ANSWER
Yes; the diagonals bisect each other. f.
No; the diagonals do not
bisect each other.
ANSWER 13

14. Homework