2.4 Use Postulates & Diagrams Objectives: 1.To illustrate and understand postulates about lines and planes 2.To accurately interpret geometric diagrams

Postulates postulates This chain of logical reasoning must begin somewhere, so every deductive system must contain some statements that are never proved. In geometry, these are called postulates.

Postulates and Theorems PostulatesPostulates are statements in geometry that are so basic, they are assumed to be true without proof. axioms –Sometimes called axioms. TheoremsTheorems are statements that were once conjectures but have since been proven to be true based on postulates, definitions, properties, or previously proven conjectures. Both postulates and theorems are ordinarily written in conditional form.

Postulates Postulate 1: Ruler Postulate Pg 9 Postulate 2: Segment Addition Postulate Pg 10 Postulate 3: Protractor Postulate Pg 24 Postulate 4: Angle Addition Postulate Pg 25

Postulates

Example 1 State the postulate illustrated by the diagram.

Example 2:Identify postulates from a diagram Use the diagram to write examples of Postulates 9 and 11. Q W, V, and YPostulate 9:Plane Q contains at least three noncollinear points, W, V, and Y. line bPostulate 11:The intersection of plane P and plane Q is line b.

Use the diagram to write examples of Postulates 9 and 10. Postulate 9 : Plane P contains at least three noncollinear points, A, B, and C. Postulate 10 : Point A and point B lie in plane P, so line n containing A and B also lies in plane P.

Use the diagram to write examples of Postulates 6 and 8 P6:Line l contains at least two points R and S Postulate 8: Through noncollinear points R, S, and W, there exists exactly one plane M

Use the diagram to write examples of Postulates 5 and 7 Which postulates are shown in the following diagram?

Checkpoint Using the diagram, which postulate allows you to say that the intersection of line a and line b is a point? Postulate 7Postulate 7

Interpreting Diagrams When you interpret a diagram, you can assume only information about size or measure if it is marked.

Interpreting Diagrams

Perpendicular Figures perpendicular to a plane A line is perpendicular to a plane if and only if the line intersects the plane in a point and is perpendicular to every line in the plane that intersects it at that point.

Example Which of the following cannot be assumed from the diagram? 1.A, B, and F are collinear. 2.E, B, and D are collinear. 3.AB  plane S

Example Which of the following cannot be assumed from the diagram? 4.CD  plane T 5.AF intersects BC at point B.

Assignment Pg 99 # 3 – 23 (# 11-13, don’t give real world example. If false, draw a picture of a counterexample)