Chapter 1
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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

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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


Chapter 1

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


Chapter 1

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


Chapter 1

Area

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


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