1. Chapter 1 Tools Of Geometry

2. Drill
1, 3, 5, 7, 9, __, __
2, 5, 8, 11, 14, __, __
-3, -6, -10, -15, ___
, , , ___

3. 1.1 Using Patterns and Inductive Reasoning

4. Notes
Inductive Reasoning: Allows you to reach conclusions based on a pattern of specific examples.
Ex: Someone eating the same breakfast everyday.

5. Conjecture: A conclusion reached using inductive reasoning.
Example: Make a conjecture about the shapes.

6. Points
Regions 2 3 4 5 6

7. Use Inductive Reasoning To find the sum of the first 20 odd numbers
= 1
= 4
= 9
= 16
= 25

8. 1.2 Points, Lines, and Planes

9. Drill Find the next number in the sequence: -3, -1, 1, 3, __, __
1, 4, 2, 5, 0, __, __
Name three things in the real world that represent a line, a point and an angle.

10. Notes(Vocab)
Points: have no size, often represented with dots, and named with a capital letter. C A B

11. Lines: have no thickness, and extend infinitely in two directions
Lines: have no thickness, and extend infinitely in two directions. Named with two points, or a cursive letter. l Y X

12. Collinear: points that are lying in the same line.
Non-Collinear: Not lying in the same line. A B C C A B

13. Planes: Extend infinitely in all directions
Planes: Extend infinitely in all directions. It is flat and has no thickness. There are two ways to name a plane.
To Name a plane you need 3 non-collinear points.
Coplanar: Points and lines that are in the same Plane.

14. Postulates: an accepted statement or fact.
*The intersection of two lines is a ______ *The intersection of two planes is a ______ *Through any two points lies exactly one ______ *Through any three non-collinear points there is exactly one ______.
point
line
line
plane

15. A C B I D E H F G

17. Drill Two planes intersect to make a ___.
Two lines intersect to make a ___.
How many different ways can you name this line?
A B C D

18. 1.3 Segments, Rays, Parallel Lines and Planes

19. Segments: Are parts of lines, they have two endpoints, and are named by using the two endpoints.

20. Rays: is a “half-line”. It has one endpoint and extends infinitely in one direction.
Opposite Rays: share the same endpoint and go in opposite directions.

21. Parallel Lines: are lines that are in the same plane and do not intersect.

22. Parallel Planes: Two planes that never intersect.
Skew Lines: Lines that do not intersect but are not parallel, because they are in different planes.

23. A C B I D E H F G