2.4 Use Postulates & Diagrams2.4 Use Postulates & Diagrams

Objectives:

1.To illustrate and understand postulates about lines and planes

2.To accurately interpret geometric diagrams

PostulatesPostulates

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 postulatespostulates.

Postulates and TheoremsPostulates and Theorems

• PostulatesPostulates are statements in geometry that are so basic, they are assumed to be true without proof.– Sometimes called

axiomsaxioms.

• 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 1 - 4Postulates 1 - 4

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 5 - 11Postulates 5 - 11

Example 1Example 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.

• Postulate 9:Plane QQ contains at least three noncollinear points, W, V, W, V, and and YY.

• Postulate 11:The intersection of plane P and plane Q is lineline b b.

Use the diagram to write examples of Postulates 9 and 10.

Postulate 9: Plane P contains atleast 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 Use the diagram to write examples of Postulates 5 and 7examples 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 DiagramsInterpreting Diagrams

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

Interpreting DiagramsInterpreting Diagrams

Interpreting DiagramsInterpreting Diagrams

Perpendicular FiguresPerpendicular Figures

A line is perpendicular perpendicular to a planeto 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 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 Example

Which of the following cannot be assumed from the diagram?

4.CD plane T

5.AF intersects BC at point B.

AssignmentAssignment

Pg 99# 3 – 23

(# 11-13, don’t give real world example. If false, draw a picture of a counterexample)