Ch. 1-1Points, Lines, and Planes

Mr. Schaab’s Geometry ClassOur Lady of Providence Jr.-Sr. High

School 2015-2016

Undefined Terms

The three most basic figures in the world of Geometry are so simple that there is no formal definition for them!

Throughout the semester, we will use these three figures to create many other figures, shapes, and surfaces.

They are: Point, Line, and Plane

Point

A point, in reality, is nothing more than a location.

We represent points using dots, but points actually have no size. In other words, a point has zero dimensions.

To name a point, we always use a CAPITAL letter.

Line A line, much like a point, is more of an idea

that a tangible object. A line only has length. We represent lines

with width so that we can see them. We also put arrowheads on each end of a line

to show that it extends forever in both directions.

To name a line, we have two options. We can use two points on the line, or we can use a lower case letter .

Plane A plane is a flat surface that extends

forever in all directions. A plane has width and length, but it

has no depth, or thickness. We represent planes by drawing a

square, rectangle, or parallelogram.

To name a plane, we also have two options. We can use a capital letter (Plane P), or we can use three points on the plane that do not lie on the same line. (Plane ABX)

Try it!1. Give another

name for line g.

2. Give another name for Plane F.

3. Name two points that are not on plane F.

Line BC, Line CB, Line DB, Line BD, Line CD, Line DC.

Plane ABE, Plane AEB, Plane BEA, Plane BAE, Plane EBA, Plane EAB

C and D

Collinear and Coplanar

Collinear points – points that lie on the same line.› Since a line is defined by two points, two

points anywhere in the universe are always collinear…there is always a line that will pass through both of them.

Coplanar points – points that lie on the same plane.› Since a plane is defined by three points,

three points anywhere in the universe are always coplanar…but not necessarily collinear.

Defined Terms

Using our 3 undefined terms, we can create all of the shapes and objects that make up the study of Geometry!

Segment – a small section of a line. Segments always have two endpoints.

Ray – Section of a line with only one endpoint.

Defined Terms

Important! Segments and rays can also be collinear or coplanar!› Ex: opposite rays – two rays that share

an endpoint and extend forever in opposite directions.

› If a line contains 3 points, you can always name a pair of opposite rays, but be careful naming them!

Intersections The intersection of two figures is the

point or points they have in common.› Ex: the intersection of

two lines is a point (C).

› Ex: the intersection of two planes is a line (l).

Challenge

On the back of your definition sheet, sketch the following geometric figures:a) A plane with two intersecting lines that

intersect the plane at different points

b) A plane and two intersecting lines that do not intersect the plane

c) A plane and two intersecting lines that both lie in the plane.

Postulates!

Postulate is a fancy word for a statement that is widely accepted as being true.› Another fancy word for it is an axiom.

Postulate 1-1: through any two points there is exactly one line.

Postulate 1-2: through any three non-collinear points there is exactly one plane.

More Postulates!

Postulate 1-3: if two different lines intersect, they intersect in exactly one point.

Postulate 1-4: if two different planes intersect, they intersect in exactly one line.

Now try to sketch an example of each postulate!

Homework…YAY!

iTeach -> Mr. Schaab -> Geometry -> Homework

Complete 1-1 HW #1-20 in the Practice section and #1-4 in the Applications section.

Your first Homework Quiz will be Tuesday (A) or Wednesday (B)!

Remember, you may use your homework on the HW Quiz so you might want to copy the pictures onto your homework or print it out.