- Submitted By: Aaron-Penington
- Date Submitted: 04/22/2014 8:54 PM
- Category: Miscellaneous
- Words: 1481
- Page: 6

Chapter 1 Tools of Geometry

Lesson 1 Patterns and Inductive reasoning

Using Inductive Reasoning

Inductive Reasoning is based on observed patterns.

1, 3, 5, 7, 9 . . .

A Conjecture is the conclusion you reach using inductive reasoning.

Example: Make a conjecture about the sum of the first 30 odd numbers.

1 = 1 =12

1+3 =4 = 22

1+3+5 =9 = 32

1+3+5+7 =16= 42

1+3+5+7+9 =25= 52

What is the sum of the first 30 odd numbers?

302 =900

Chapter 1 Tools of Geometry

Lesson 1 Patterns and Inductive reasoning

A Conjecture is the conclusion you reach using inductive reasoning.

Not all conjectures are true! You can prove that a conjecture is false by finding one counterexample.

A Counterexample is an example for which a conjecture is false.

Example: Find a counterexample.

A)Any three points can conect to make a triangle.

Conjecture counterexample

B)Adding two numbers together will give you a sum larger than either of the original two numbers.

4+3=7 (-2)+(-2)=(-4)

conjecture Counterexample

Chapter 1 Tools of Geometry

Lesson 2 Drawing nets and other models

Drawing isometric Views of a 3d figures

Isometric views

2d

3d your textbook

Ex: Isometric Drawings use isometric dot paper to show three sides of a figure from a corner view.

like this.

Orthographic Views

2d → ⇱

3d → a box

Orthographic drawing gives a three d showing of the top view, front view, and right side view.

Drawing a net

A net is a 2d pattern that you can fold to form a 3d figure.

To draw a net

Label the faces and bases

Draw one base, one face that connects both bases, the other base and the remaining faces.

Example:

Chapter 1 Tools of Geometry

Lesson Points, Lines, and Planes...