Geometry Geo- Earth -metry Measure Geometry- “Earth Measure”

Definition Geometry Study of relationships between points, lines, planes and solids.

The system was first written down by a Greek man named Euclid. The Geometry that we will study this year is called Euclidean Geometry.

Terms we accept without definition Category 1 Undefined Terms Terms we accept without definition 3 types Point Line Plane

Many types that we will study during this course Category 2 Defined Terms Definition- Terms that have a definition Many types that we will study during this course

Postulates Category 3 Definition- Euclid Today Statements that we accept without proof Euclid Had 5 postulates Today We have many more

Undefined Term 1 Point Name a point with a capital letter Has no length, width or thickness Indicates a position or place Name a point with a capital letter Ex. A X Y

Undefined Term 2 Line Points grouped next to each other to form a straight line Has length but no width or thickness

Naming a Line 1 Using two points on the line Ex. Pick any two in any order Ex. C Can be named in the following ways with any two of the letters. Notice the double arrows above the letters B A BC AB AC

Try This Name the following line in three different ways Ex. Z Y X

Naming a line 2 l Use a lowercase cursive letter Ex. Line l Letter is not a point on the line Letter stands for all the points on the line Ex. Line l l

Undefined Term 3 Plane Set of points that form an infinite surface Infinite means goes on forever

Naming a Plane Use a capital letter in the corner of the plane The letter is not a point Use this figure to represent a plane Remember the plane continues in all directions A Plane A

Defined Terms Reminder Defined terms are terms that have a definition They are the second category in the Geometry System

Defined Terms cont. Collinear points Definition: all the points on a line Any two points are collinear because they can both be on the same line More than two points can be collinear, but do not have to be collinear

Ex. E D A C B Any two points are collinear in this diagram ie: A and E; B and C; D and A; and so on Three points that are collinear are B C and D However Points A, B and D are not collinear In this case A, B and D are called Noncollinear

Defined Terms cont. Noncolinear Ex. Definition: Points that are not contained on the same line In this case A, C and D are called Noncollinear Ex. A D C

Defined Terms cont. Coplanar Noncoplanar Definition: points all in the same plane Noncoplanar Definition points not in the same plane Example: The Rectangular Prism

Points A, B, C and D are coplanar Points A, B, C and H are noncoplanar F G H Ex. Points A, B, C and D are coplanar Points A, B, C and H are noncoplanar

Ray Definition: A part of a line that has one endpoint and all the points on one side of the endpoint Could also be said that it is Half of a line Naming a Ray The endpoint of the ray must be the first letter followed by any letter(s) on the line. The Name has a one way arrow above the letters

X must always be first in this case because it is the endpoint Example Z Y This Ray can be called: XY XZ XYZ X must always be first in this case because it is the endpoint X

Line Segment Naming a Line Segment Definition: A part of a line that has 2 endpoints and includes all of the points between the endpoints Naming a Line Segment Use the two endpoints in any order with a line above the name

This Line Segment can be called: Example Z Y This Line Segment can be called: XZ ZX XYZ ZYX X or Y must always be first or last in this case because they are the endpoints X

Try This Given ray QM Given Line Segment AZ Is Z on this ray? Is A on this ray? Given Line Segment AZ Is Q on this segment? Is ray QZ on this segment Z M Q A

Solutions Given ray QM Given Line Segment AZ Is Z on this ray? Yes Is A on this ray? No, point A is past the endpoint Q and is not on the ray QM Given Line Segment AZ Is Q on this segment? Is ray QZ on this segment No, ray QZ has points that are past the endpoint Z on the line segment AZ

Postulates Through any two points there is exactly one line A B C

Postulates Through any three non collinear points there is exactly one plane C B A

Postulates If two points lie in a plane then the line containing them also lies in that plane C B

Postulates If two planes intersect their intersection is a line A B l

Postulate If two lines intersect, then the intersect at exactly one point l P m