Identify, name, and draw points, lines, segments, rays, and planes.

Apply basic facts about points, lines, and planes.

Objectives

Points, Lines and Planes

undefined term point

line plane

collinear coplanar

segment endpoint

ray opposite rays

postulate

Vocabulary

Points, Lines and Planes

The most basic figures in geometry are undefined terms, which cannot be defined by using other figures.

Point These are theLine building blocksPlane of geometry

Points, Lines and Planes

● A Point is simply a location

Vocabulary

Points, Lines and Planes

● A Line is made up of points and has no thickness or width. Points on the same line are said to be collinear.

AB

CD

These points are collinear

Vocabulary

Points, Lines and Planes

A Plane is a flat surface made up of points. Points that lie on the same plane are said to be coplanar. A plane has no depth and extends infinitely in all directions.

Vocabulary

Points, Lines and Planes

Points, Lines and Planes

A line containing point NThe line can be named as line c.There are three points on the line. Any two of the points can be used to name the line.

NOOMMONMMN

Example 1 – Name Lines and Planes

M

N

O

P

cA

A plane containing points P and M• The plane can be named as plane A.• You can also use the letters of any three

noncollinear points to name the plane.• Examples: plane MNP plane MOP plane NOP.• There are 18 different 3-letter names for this plane.

M

N

O

P

cA

Example 2 – Name Lines and Planes

Example 3 – Draw Geometric Figures

ALGEBRA Lines AB and CD intersect at E for A(-4, 3), B(2, -1), C(2, 4) and D(-4, -2) on a coordinate plane. Point G is coplanar with these points, but not collinear withor .

ABCD

5

4

3

2

1

-1

-2

-3

-4

-5

-6 -4 -2 2 4 6

A

C

BD

G

Example 4 – Draw Geometric Figures

lies in plane P and contains point Y

P X

Y

W

Example 5 – Draw Geometric Figures

a. How many planes appear in this figure?

X

Y

Z

Q

T

R

P

Example 5 – Draw Geometric Figures

b. Name three points that are collinear.

X

Y

Z

Q

T

R

P

Example 5 – Draw Geometric Figures

c. Are points X, Y, Z, and P coplanar? Explain.

X

Y

Z

Q

T

R

P

Example 6 – Draw Geometric Figures

d. At what point do lines PR and TZ intersect?

X

Y

Z

Q

T

R

P

Draw and label each of the following.

A. a segment with endpoints M and N.

B. opposite rays with a common endpoint T.

Understanding Points, Lines and Planes

Example 7 – Draw Geometric Figures

Understanding Points, Lines and Planes

Example 8 – Draw Geometric Figures

Draw and label a ray with endpoint M that contains N.

A postulate, or axiom, is a statement that is accepted as true without proof. Postulates about points, lines, and planes help describe geometric properties.

Understanding Points, Lines and Planes

Understanding Points, Lines and Planes

Name a line that passes through two points.

Example 9

Understanding Points, Lines and Planes

Name a plane that contains three noncollinear points.

Example 10

Understanding Points, Lines and Planes

Understanding Points, Lines and Planes

A. Sketch two lines intersecting in exactly one point.

B. Sketch a figure that shows a line that lies in a plane.

Example 11 - Representing Intersections

Understanding Points, Lines and Planes

Sketch a figure that shows two lines intersect in one point in a plane, but only one of the lines lies in the plane.

Understanding Points, Lines and Planes

Example 12 - Representing Intersections

1. Two opposite rays.

3. The intersection of plane N and plane T.

4. A plane containing E, D, and B.

2. A point on BC.

Understanding Points, Lines and Planes

Example 13

A line intersecting a plane at one point

A ray with endpoint P that passes through Q

Draw each of the following.

Understanding Points, Lines and Planes

Example 14