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Chapter 1. Reasoning in Geometry. Section 1-1. Patterns and inductive reasoning. Inductive Reasoning. When you make a conclusion based on a pattern of examples or past events. Conjecture. A conclusion that you reach based on inductive reasoning. Counterexample.

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chapter 1

Chapter 1

Reasoning in Geometry

section 1 1
Section 1-1

Patterns and inductive reasoning

inductive reasoning
Inductive Reasoning

When you make a conclusion based on a pattern of examples or past events

conjecture
Conjecture

A conclusion that you reach based on inductive reasoning

counterexample
Counterexample

An example that shows your conjecture is false

It only takes one counterexample to prove your conjecture false

examples
Examples

Find the next three terms of each sequence.

11.2, 9.2, 7.2, …….

1, 3, 7, 13, 21, …….

……..

section 1 2
Section 1-2

Points, lines and planes

point
Point

A basic unit of geometry

Has no size

Named using capital letters

slide9
Line

A series of points that extends without end in two directions.

Named with a single lowercase letter or by two points on the line

collinear and noncollinear
Collinear and Noncollinear

Points that lie on the same line

Points that do not lie on the same line

slide11
Ray

Has a definite starting point and extends without end in one direction

Starting point is called the endpoint

Named using the endpoint first, then another point

line segment
Line Segment

Has a definite beginning and end

Part of a line

Named using endpoints

plane
Plane

A flat surface that extends without end in all directions

Named with a single uppercase script letter or three noncollinear points

coplanar and noncoplanar
Coplanar and Noncoplanar

Points that lie in the same plane

Points that do not lie in the same plane

section 1 3
Section 1-3

postulates

postulates
Postulates

Facts about geometry that are accepted as true

postulate 1 1
Postulate 1-1

Two points determine a unique line

postulate 1 2
Postulate 1-2

If two distinct lines intersect, then their intersection is a point.

postulate 1 3
Postulate 1-3

Three noncollinear points determine a unique plane.

postulate 1 4
Postulate 1-4

If two distinct planes intersect, then their intersection is a line.

section 1 4
Section 1-4

Conditional statements and their converses

conditional statement
Conditional Statement

Written in if-then form

Examples:

Ifpoints are collinear, then they lie on the same line.

Ifa figure is a triangle,then it has three angles.

If two lines are parallel, then they never intersect.

hypothesis
Hypothesis

The part following the if

If points are collinear, then they lie on the same line.

If a figure is a triangle,then it has three angles.

If two lines are parallel, then they never intersect.

conclusion
Conclusion

The part following the then

If points are collinear, then they lie on the same line.

Ifa figure is a triangle,then it has three angles.

If two lines are parallel, thenthey never intersect.

converse
Converse

A conditional statement is formed by exchanging the hypothesis and the conclusion in a conditional statement

example
Example

Statement: If a figure is a triangle, then it has three angles.

Converse: If a figure has three angles, then it is a triangle.

section 1 6
Section 1-6

A plan for problem solving

perimeter
Perimeter

The distance around a figure

formula
Formula

An equation that shows how certain quantities are related

slide30
Area

The number of square units needed to cover the surface of a figure

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