Geometry!

• What did the acorn say when it grew up? • This will be fun. . . believe it or not, but there will be some work involved as well

• You will need:– Three Ring Binder– Loose Leaf Paper

– Notebook• We will be keeping a vocabulary notebook

throughout the course of the year• We will also be doing some labs, these you

will get done in class, so don’t worry

Lesson 1Points, Lines, and Planes

Warm-Up Problems

• Vocabulary: The _________ Plane contains the x-axis and y-axis.

• Kira needs to buy a piece of pipe that is 40% longer than the 7 inch piece she already has. What length of pipe does she need?

• Evaluate: 4(n+6) For n=2

2n

• Simplify:

New Concepts

• Undefined Term: a basic mathematical term that is not defined by using other mathematical terms– Examples: Points, Lines, and Planes

* These terms are undefined because their definitions are cyclic, that is, the word being defined is in the definition.

• Point: names a location and has no size. It is represented by a dot and labeled using a capital letter. P

Lines

• Line: a straight path with no thickness which extends forever. – There are an infinite

number of points on a line

– A line is named using either a lowercase letter or by using any two points located on the line.

• Any set of points on the same line are called collinear points (A, C, and D)

• Points that do not lie on the same line are noncollinear (A,B,C)

A C D x

B

Example

• Give 2 different names for this line

• Name three collinear points and three noncollinear points

F

R

D

E

y

O

Planes!!

Not that kind. . .

This kind of Plane!

• Plane: a flat surface that has no thickness and extends forever– Named using either an uppercase letter or three noncollinear points that

lie in the plane

Example 1

• What are 2 Possible names for this plane?

More Planes

• Lines or points that lie in the same plane are said to be coplanar

• If there is a line that does not lie on the plane that contains other lines or points they are noncoplanar

• Space is the set of all points, therefore, space includes all lines and all planes

Example 2 *Pretend there is a line

connecting points S and P• Indentify the coplanar

and noncoplanar lines in this plane

• This plane is an example of an intersection which is the point or set of points in which two figures meet. – Plane intersection = line– Line intersection = point– Line on a plane = line– Line through a plane =

point

Example 3

• Where do lines l and m intersect on Plane X?

Example 4

Name all of the different intersections you see in the two diagrams and identify

where they meet

Bonus Question

Is it possible to draw a point on a piece of paper which would fit the definition of

point?

• No, since the inked dot on a piece of paper has a given area and dimension. The definition of a point is that it has no size and is a

zero-dimensional object