9B - 12 / 2 / 2008

In the beginning of the class we review what we learned yesterday:
- Definition of parallelograms: Both pairs of opposite sides are parallel
- Theorem 6-1: Opposite sides of a parallelogram are congruent.
- Theorem 6-2: Opposite angles of a parallelogram are congruent
- Theorem 6-3: Consecutive angles of a parallelogram are supplementary
- Theorem 6-4: The diagonals of a parallelogram bisect each other
Then we corrected the homework that was due today.

Somethings to remember that we used in the hw and will be on future tests:
1- To check if the diagonals are congruent or bisect each other you will need to calculate FOUR distance formulas.
2- Diagonals are NOT necessarily congruent but BISECT each other.
3- We saw a new method to calculate the possibilities for the forth point of a quadrilateral using logical reasoning and slopes.
4- You have to closely observe the diagrams and look for relations between the angles and the sides in the figure in order to get some of the answers asked.

You might have noticed that until now all theorems of chapter 6 have a given info that is a parallelogram and that leads to a conclusion of other fact. So, today we learned 4 new Theorems that do the opposite: give you the information and leads to the fact that it is a parallelogram.


Today's Lesson:
- Theorem 6-5: If both pairs of sides are congruent, then it is a parallelogram. (converse of T 6-1)
- Theorem 6-6: If both pairs of opposite angles are congruent, then it is a parallelogram. (converse of T 6-2)
- Theorem 6-7: If the diagonals bisect each other, then it is a parallelogram. (converse of T 6-4)
- Theorem 6-8: ONE pair of opposite sides is BOTH congruent AND parallel, then it is a parallelogram.

Notice that there is no converse for Theorem 6-3.
For this chapter you must know all quadrilateral properties in order to succed in quizzes, tests, and the rest of your life!

There is homework due tomorrow: Pg. 301- #15-32 all


Have a great week!
Get better Mrs. Saatkamp!
See you on Monday!
Giovanna Dedini (GD)