Section 2.5

Postulates and Paragraph Proofs

Postulate or axiom- a statement that is accepted as true

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

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 entire line containing those points lies in that plane

2.6 If two lines intersect, then their intersection is exactly one point

2.6 If two planes intersect, then their intersection is a line

Theorem- once a statement or conjecture has been shown to be true

Proof-is a logical argument in which each statement you make is supported by a statement that is accepted as true

Paragraph proof- write a paragraph to explain why a conjecture for a given situation is true

Key Concept

1. State the theorem or conjecture to be proven
2. List the given information
3. If possible, draw a diagram to illustrate the given information
4. State what is the be proved
5. Develop a system of deductive reasoning

[__]=Vocabulary


[__]=Postulates