1. Lesson 8.3: Show that a Quadrilateral is a Parallelogram
Geometry

2. Theorem 8.7: Side Congruence Theorem
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Converse of Theorem 8.3

3. Theorem 8.8: “Angle Congruence Theorem”
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Converse of Theorem 8.4

4. Theorem 8.9: “Congruent Parallel Theorem”
If one pair of opposite sides of a quadrilateral are congruent AND parallel, then the quadrilateral is a parallelogram.

5. Theorem 8.10: “Diagonal Bisect Theorem”
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

6. Summary: Ways to Prove a Quadrilateral is a Parallelogram
Show both pairs of opposite sides are parallel. [Definition of Parallelogram]
Show both pairs of opposite sides are congruent. [Side Congruence Th.]
Show both pairs of opposite angles are congruent. [Angle Congruence Th.]
Show one pair of opposite sides are congruent and parallel. [Congruent Parallel Th.]
Show the diagonals bisect each other. [Diagonal Bisect Th.]

7. Examples
What theorem can you use to show that the quadrilateral is a parallelogram?

8. Check Your Progress
What theorem can you use to show that the quadrilateral is a parallelogram?

9. Warm-Up Find the slope of the line that passes through the points
Find the midpoint of the segment that begins at and ends at
Find the distance between the points

10. Angle Congruence Th.
Side Congruence Th.
Diagonal Bisect Th.
Congruent Parallel Th.

11. Board Points 30 point grade
Each time you go to the board and complete a problem, explain you problem to the class and have the correct work and answer, you will receive 6 points.
You need at least 5 visits to the board in order to receive the 30 points.
Any additional boards points after 5 will be worth 3 extra credit points per problem.
You will have until May 5th to go up 5 times (most likely one chance per week).

12. Lesson 8.3: Show that a Quadrilateral is a Parallelogram (part 2)
Geometry

13. Prove that a Quadrilateral is a Parallelogram on a Coordinate Plane
Given the ordered pairs of the vertices of a quadrilateral, you can prove whether the quadrilateral is a parallelogram or not.
Some Concepts to remember:
Slope
Distance Formula
Midpoint Formula

15. How to Prove a Quadrilateral is a Parallelogram on a Coordinate Plan
DEFINITION OF PARALLELOGRAM
Find Slope of all 4 sides. Opposite sides need to have equal Slope.
SIDE CONGRUENCE THEOREM
Find distance of all 4 sides. Opposite sides need to be equal in distance.
CONGRUENT PARALLEL THEOREM
Find Slope of one pair of opposite sides. They need to be equal.
Find distance of the same pair of opposite sides. They need to be equal.

16. Homework WED 3/16: THU 3/17 Workbook Pg. 151 Textbook Pg. 523
#1-10 (all)
Textbook Pg. 523
#2-7 (all)
THU 3/17
Worksheet Packet
8.1: #7-25 (odd)
8.2: #5, (odd)
8.3: #1-13 (odd)