2.5: Postulates and Paragraph Proofs

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

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

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

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

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

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

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

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

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

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

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