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...