1. Points, Lines, Planes, Segments and Midpoints
Tools of Geometry

2. Undefined Terms
Undefined terms are things that can only be described or explained using examples.
Points, line, and planes are examples of undefined terms.
Where can we find examples of points, lines, or planes in life?

3. Points
A point is a location
A point is named by a capital letter

4. Lines
A line is made up of points and has no thickness; there is exactly one line through any two points
A line is named by the letters representing the two points on the line or a lowercase script letter

5. Planes
A plane is a flat surface made up of points that extends infinitely in all directions. There is exactly one plane through any three non-collinear points.
A plane is named by a capital script letter or by the letters naming three points that are not on the same line

6. Examples

7. Intersection
An intersection of two or more geometric figures is the set of points they have in common.
Two lines intersect in a point; two planes intersect in a line.

8. Examples

9. Line Segment
A line segment can be measured because it has two endpoints
A segment is named for its endpoints

10. Example

11. Number Line
Distance Formula =

12. Coordinate Plane Distance Formula =
This formula is the same as the Pythagorean Theorem, it just looks slightly different.

13. Examples

14. Midpoint
The midpoint is the point that is halfway between the endpoint.
On a number line:
In a coordinate plane:

15. Examples
Find the coordinates of G if P is the midpoint of for E(-8,6) and P(-5,10)

16. Examples

17. Segment Bisector
Any segment, line, or plane that intersects another segment at its midpoint.

18. Fractional Distances
Just like the midpoint is halfway (1/2) from one end to the other, other fractional distances can be calculated
Pay close attention to WHERE the point is located; from A to B is different than from B to A

19. Examples

20. Questions What are the undefined terms?
How can we use these concepts in real life?
Are there any jobs that might require the use of these concepts?
See if you can find any other careers that may use these concepts.