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

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

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

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

5. 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

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

7. 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

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

9. 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

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

11. 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

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

13. 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

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

15. 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

16. 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

17. 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

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

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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

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

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

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

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

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