1. 2.5: Postulates and Paragraph Proofs

2. Postulates (also called axioms):
Statements that describe a fundamental relationship that is accepted to be true (no proof necessary)

3. The Segment Addition Postulate
If B is between A and C then
AB + BC = AC

4. Theorems:
A statement proven to be true by using undefined terms, definitions and postulates

5. Basic Geometric Postulates
2.1: Through any two points there is exactly one line
2.2 Through any three points not on the same line, there is exactly one plane

6. Basic Geometric Postulates
2.3: A line contains at least two points
2.4: A plane contains at least three points, not on the same line
2.5: If two points lie in a plane, then the line that contains those points is in the plane

7. Basic Geometric Postulates
2.6: If two lines intersect, then their intersection is exactly one point
2.7: If two planes intersect, then their intersection is a line

8. Practice: S/A/N True Line GH contains three non collinear points
Never True
For line XY, if X lies in plane Q and Y lies in plane R, then plane Q intersects plane R
Sometimes True

9. It’s Proof Time!!
Proof: A logical argument in which each statement made is supported by a statement known to be true

10. Write instructions in a paragraph
1) Mr. T to turn off the lights from his seat
2) Jake to erase the “X” on the board from her seat

11. Paragraph Proof/Informal Proof:
A paragraph that explains why a conjecture for a given situation is true

12. If M is the midpoint of AB, then AM = ½ AB
The Midpoint Theorem:
If M is the midpoint of AB, then AM = ½ AB