1. 2.5 Postulates and Proofs GEOMETRY

2. Postulate (axiom)- a statement that is accepted as true without proof 2.1: Through any two points, there is exactly one line 2.2: Through any three noncollinear points, there is exactly one plane

3. 2.3: A line contains at least 2 points 2.4: A plane contains at least 3 noncollinear points

4. Postulates 2.5: If two points lie in a plane, then the entire line containing those points lies in the plane 2.6: If two lines intersect, then their intersection is exactly one point 2.7: If two planes intersect, then their intersection is exactly one line

5. Example 1 Determine whether each statement is always, sometimes, or never true. Explain. A. If plane T contains line EF and line EF contains point G, then plane T contains point G. B. Line GH contains 3 noncollinear points.

6. Proof- a logical argument in which each statement is supported by a statement that is accepted as true Theorem- a statement or conjecture that has been proven and can be used as a reason to justify other proofs. Paragraph proof- informal proof written in paragraph form

7. The Proof Process 1) List the given info, and if possible draw a diagram. 2) State the theorem or conjecture to prove. 3) Create a deductive argument by forming a chain of statements. 4) Justify each statement with a reason (definitions, algebraic properties, postulates, and theorems) 5) State what has been proved.

8. Example 2 Given line AC intersects line CD, write a two-column proof to show that A, C, and D are noncollinear.

9. assignment Worksheet