1. Deductive Reasoning

2. The Law of Detachment This applies when one statement is conditional and a second statement confirms the hypothesis of the conditional. The conclusion is then confirmed. Here is an example.

3. Deductive Reasoning
Mary goes to the movies every Friday and Saturday night. Today is Friday. What conjecture can you make from the above statements?

4. The Law of Syllogism
This applies when you have two conditional statements. The conclusion of one, confirms the hypothesis of the other. In this case our result is still a conditional with the first hypothesis and the second conclusion.
(I call this the “Oreo Cookie” Law.) Here is how it works…

5. Deductive Reasoning
If Rick takes chemistry this year, then Jesse will be Rick’s lab partner. If Jesse is Rick’s lab partner, then Rick will get an A in chemistry.
Combine the two above conditional statements into one conditional statement.

6. Deductive Reasoning
If a polygon is regular, then all angles in the interior of the polygon are congruent. If a polygon is regular, then all of its sides are congruent.
Why can’t these two statements be combined like the last example.

7. Postulate: Through any two points there exists exactly one line.

8. Postulate: A line contains at least two points.

9. Postulate: If two lines intersect, then their intersection is exactly one point.

10. Postulate: Through any three noncollinear points there exists exactly one plane.

11. Postulate: A plane contains at least three noncollinear points.

12. Postulate: If two points lie in a plane, then the line containing them lies in the plane.

13. Postulate: If two planes intersect, then their intersection is a line.