# Warmup Warmup Warmup Warmup Agenda n n n

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Warm-up

Warm-up

Warm-up

Warm-up

Agenda n n n Return Plane Picture Project Chapter 2 Connecting Reasoning and Proof Homework

2 -1 Inductive Reasoning and Conjecturing Definition Inductive Reasoning – Reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction. Conclusions arrived at by inductive reasoning lack the logical certainty of those arrived at by deductive reasoning.

Real-life Examples 1. Given: Suzie did not do her chores. 2. Conjecture: Suzie will not be allowed to go to the mall with her friends. 2. Given: Billy did not study for his Geometry test. 3. Conjecture: Billy will not do well on his test. 4. Billy will flunk Geometry. 5. Billy will drop out of high school. 6. Billy will live in a cardboard box behind the ACME.

Geometry Examples

Geometry Examples

Geometry Examples

A Proper Conjecture?

2 -1 Study Guide

2 -2 If-Then Statements and Postulates p – hypothesis q – conclusion – negation

Example (p q ) (q p) ( p q) ( q p)

2 -2 Additional Postulates Postulate 2 -1 Through any two points, there is exactly one line. Postulate 2 -2 Through any three points not on the same line, there is exactly one plane. Postulate 2 -3 A line contains at least two points.

2 -2 Additional Postulates Postulate 2 -4 A plane contains at least three points not on the same line. Postulate 2 -5 If two points lie in a plane, then the entire line containing those two points lies in that plane. Postulate 2 -6 If two planes intersect, then their intersection is a line.

2 -2 Venn Diagrams Human Beings Students RV Americans