Chapter 1 Tools Of Geometry

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

1.1 Using Patterns and Inductive Reasoning

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

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

Points Regions 2 3 4 5 6

Use Inductive Reasoning To find the sum of the first 20 odd numbers 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 + 9 = 25

1.2 Points, Lines, and Planes

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.

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

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

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

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.

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

A C B I D E H F G

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

1.3 Segments, Rays, Parallel Lines and Planes

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

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.

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

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

A C B I D E H F G