Geometry

1.1 Points, Lines,

and Planes

1.1 Warm-up

Solve for the variable.

1. 2. 3.

4. 5. 6.

Essential Question

What are the three undefined terms and what is important about these three objects?

August 15,

2016Geometry 1.1 Points, Lines and Planes

What Will You Learn?

• Understand and use the basic undefined terms and defined termsof geometry.

• Sketch the intersection of lines and planes.

• Solve real-life problems involving lines and planes.

August 15,

2016Geometry 1.1 Points, Lines and Planes

Where Do We Start?

August 15,

2016Geometry 1.1 Points, Lines and Planes

What are these terms?

Undefined Terms

• Point

• Line

• Plane

Defined Terms

• Collinear Points

• Coplanar Points

• Line Segment

• Ray

• Opposite Rays

• Coplanar

August 15,

2016Geometry 1.1 Points, Lines and Planes

3 Undefined Terms

Point: A point has no dimension. It only has location. A dot represents a point. Points are named by a capital letter.

Name:

August 15,

2016Geometry 1.1 Points, Lines and Planes

3 Undefined Terms

Line: A line has one dimension. It is a straight, unbroken set of points that goes on forever. It has length, but no thickness.

It is represented by a line with two arrowheads.

August 15,

2016Geometry 1.1 Points, Lines and Planes

l

A B

3 Undefined Terms

Line:

Through any two points, there is exactly one line.

You can use any two points on a line to name it or you can use a single italicized letter written at the end of the line.

Names:

August 15,

2016Geometry 1.1 Points, Lines and Planes

l

A B line AB

line BA

AB

BA

line l 𝑙

3 Undefined Terms

Plane: A plane has two dimensions. It is a flat surface with length and width but no thickness.

August 15,

2016Geometry 1.1 Points, Lines and Planes

MA

B C

3 Undefined Terms

Plane:

Through any three points not on the same line, there is exactly one plane.

You can use three points that are not all on the same line to

name a plane or use a capital italicized letter written in the corner.

Names: plane ABC

plane M

August 15,

2016Geometry 1.1 Points, Lines and Planes

MA

B C

Definitions

Line Segment: A segment consists of two endpoints on a line and all of the points between them.

Segments are named using the endpoints.

Names:

August 15,

2016Geometry 1.1 Points, Lines and Planes

Segment RS

Segment SR

RS

SR

R S

endpoints

Ray: A ray consists of an endpoint and all the points on a line to one side of that endpoint.

It is named by its endpoint and one other point on the ray.

Names:

August 15,

2016Geometry 1.1 Points, Lines and Planes

Definitions

M P

Initial Point

Ray MP or MP

NOT Ray PM or PM!

The initial point is always first!

Same Ray, Different Name

August 15,

2016Geometry 1.1 Points, Lines and Planes

A

B

CAB and AC

are the same

ray! They have the same initial point, and B and C are collinear.

Definitions

• Collinear: On the same line

F, Z, and P are collinear.

• Coplanar: On the same plane

B, C, and M are coplanar.

August 15,

2016Geometry 1.1 Points, Lines and Planes

F Z P

MB C

Example 1

August 15,

2016Geometry 1.1 Points, Lines and Planes

a. Name four coplanar points.

b. Name four points that are not coplanar.

c. Name three collinear points.

L, M, N, O

L, M, N, P or M, N, O, P or N, O, M, P

L, N, O

P

L

N

O

M

Example 2

August 15,

2016Geometry 1.1 Points, Lines and Planes

A B C

D

Draw three collinear points A, B, and C.

Draw point D which is not collinear with A,

B, and C. Draw 𝐴𝐵 and 𝐵𝐷.

Opposite Rays

August 15,

2016Geometry 1.1 Points, Lines and Planes

A

B

C

Opposite Rays have the same endpoint and are collinear.

CA and CB are Opposite Rays

Are these Opposite Rays?

August 15,

2016Geometry 1.1 Points, Lines and Planes

No! They

are not

collinear.

Example 3

August 15,

2016Geometry 1.1 Points, Lines and Planes

Name two pairs of opposite rays.

E F G H

Possible Answers:

,,

,,

FHFE

FGFE

GHGF

GHGE

,

,

Example 4

August 15,

2016Geometry 1.1 Points, Lines and Planes

Sketch one plane with a line in the

plane that intersects a line not in the

plane. Use the dotted line to indicate this part of the line is behind the plane.

Example 5

August 15, 2016Geometry 1.1 Points, Lines and Planes

a. Sketch a plane and a line that is in the plane.

b. Sketch a plane and a line that does not intersect the

plane.

c. Sketch a plane and a line that intersects the plane at

a point.

Example 6

August 15, 2016Geometry 1.1 Points, Lines and Planes

a. Give two other names for 𝐶𝐷.

b. Give another name for plane M.

c. Name three points that are collinear.

Then name a fourth point that is not collinear

with these three points.

Example 6

August 15, 2016Geometry 1.1 Points, Lines and Planes

d. Name a point that is not collinear with

points A, C, and E.

e. Name two pairs of opposite rays.

Essential Question Revisited

What are the three undefined terms and what is important about these three objects?

August 15,

2016Geometry 1.1 Points, Lines and Planes

Assignment

August 15,

2016Geometry 1.1 Points, Lines and Planes

1.1 worksheet