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Chapter 1

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Chapter 1

Reasoning in Geometry

Patterns and inductive reasoning

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

A conclusion that you reach based on inductive reasoning

An example that shows your conjecture is false

It only takes one counterexample to prove your conjecture false

Find the next three terms of each sequence.

11.2, 9.2, 7.2, …….

1, 3, 7, 13, 21, …….

……..

Points, lines and planes

A basic unit of geometry

Has no size

Named using capital letters

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

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

Points that lie on the same line

Points that do not lie on the same line

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

Has a definite beginning and end

Part of a line

Named using endpoints

A flat surface that extends without end in all directions

Named with a single uppercase script letter or three noncollinear points

Points that lie in the same plane

Points that do not lie in the same plane

postulates

Facts about geometry that are accepted as true

Two points determine a unique line

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

Three noncollinear points determine a unique plane.

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

Conditional statements and their converses

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.

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.

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.

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

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

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

A plan for problem solving

The distance around a figure

An equation that shows how certain quantities are related

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