1.1: Identify Points, Lines, & Planes
Objectives:
1. To learn the
terminology and
notation of the basic
building blocks of
geometry
Assignment:
• P. 5-8: 1, 5-7, 10-15,
23, 25, 39, 43, 47, 48
• Challenge Problems
You will be able to
learn terminology and the
notation of the basic
building blocks
of geometry
Objective 1
Undefined Terms?
In geometry, we always
try to define things in
simpler terms. Point,
line, and plane are
considered undefined
terms, however, and
What the Ancient
cannot be made any
Greeks said:
simpler, so we just
“A point is that which has
describe them.
no part. A line is
breadthless length.”
Undefined Terms?
In geometry, we always
try to define things in
simpler terms. Point,
line, and plane are
considered undefined What the Ancient
terms, however, and
Chinese said:
cannot be made any
“The line is divided into
simpler, so we just
parts, and that part
which has no
describe them.
remaining part is a
point.”
Undefined Terms?
Points
Lines
Planes
Basic unit of geometry
Straight arrangement of
points that extends
forever
Flat surface that extends
forever
No size, only location
No width, only length
Length and width but no
height
Named by a CAPITAL
letter: Point 𝑃
Named by two points on
the line: 𝐴𝐵 or 𝐵𝐴;
Named by a lower-case
script letter: line 𝑛
Named by a capital
script letter or 3 points
on the same plane but
not on the same line
Undefined Terms?
Points
Lines
Planes
Basic unit of geometry
Straight arrangement of
points that extends
forever
Flat surface that extends
forever
No size, only location
No width, only length
Length and width but no
height
Named by a CAPITAL
letter: Point 𝑃
Named by two points on
the line: 𝐴𝐵 or 𝐵𝐴;
Named by a lower-case
script letter: line 𝑛
Named by a capital
script letter or 3 points
on the same plane but
not on the same line
Collinear and Coplanar
Collinear points are
points that lie on the
same line.
Point 𝐴 is between
points 𝑅 and 𝑁.
Coplanar points are
points that lie on the
same plane.
Exercise 1
How many points does it take to define a
line?
How many points does it take to define a
plane?
Hierarchy of Building Blocks
3-D
2-D
1-D
Space is the
set of all points
0-D
Exercise 2
What does a sphere look like from the
perspective of a piece of paper? What if the
sphere pass through a piece of paper?
A Romance of Many Dimensions
Are there more than three spatial dimensions?
?
Point
Segment
Square
Cube
0-D
1-D (Length)
2-D (Area)
3-D (Volume)
1 point
2 points
4 points
8 points
0 “sides”
2 “sides”
4 “sides”
6 “sides”
A Romance of Many Dimensions
Are there more than three spatial dimensions?
Point
Segment
Square
Cube
0-D
1-D (Length)
2-D (Area)
3-D (Volume)
1 point
2 points
4 points
8 points
0 “sides”
2 “sides”
4 “sides”
6 “sides”
Hypercube
A Romance of Many Dimensions
Are there more than three spatial dimensions?
Point
Segment
Square
Cube
Hypercube
0-D
1-D (Length)
2-D (Area)
3-D (Volume)
4-D (Hypervolume)
1 point
2 points
4 points
8 points
0 “sides”
2 “sides”
4 “sides”
6 “sides”
A Romance of Many Dimensions
Are there more than three spatial dimensions?
Point
Segment
Square
Cube
Hypercube
0-D
1-D (Length)
2-D (Area)
3-D (Volume)
4-D (Hypervolume)
1 point
2 points
4 points
8 points
16 points
0 “sides”
2 “sides”
4 “sides”
6 “sides”
A Romance of Many Dimensions
Are there more than three spatial dimensions?
Point
Segment
Square
Cube
Hypercube
0-D
1-D (Length)
2-D (Area)
3-D (Volume)
4-D (Hypervolume)
1 point
2 points
4 points
8 points
16 points
0 “sides”
2 “sides”
4 “sides”
6 “sides”
8 “sides”
Exercise 3
1. Give two other
names for PQ and
plane R.
2. Name three points
that are collinear.
3. Name four points
that are coplanar.
Line Segment
A
B
A line segment
consists of two
endpoints and all the
collinear points
between them.
Endpoints
𝐴𝐵 or 𝐵𝐴
Ray
𝐴𝐵
A ray consists of an
endpoint and all of
the collinear points
to one side of that
endpoint.
Exercise 4
Ray BA and ray BC are considered opposite
rays. Use the picture to explain why.
C
B
A
At what time would the hands of a clock form
opposite rays?
Exercise 5
1. Give another name
for GH .
2. Name all rays with
endpoint J. Which of
these rays are
opposite rays?
E
G
J
H
F
Intersection
Two or more geometric figures intersect if they
have one or more points in common. The
intersection of the figures is the set of points
the figures have in common.
The intersection of two
lines is a point.
The intersection
of two planes is a
line.
Exercise 6
Draw plane 𝐴𝐵𝐶 that intersects plane 𝐵𝐶𝐷 at
𝐵𝐶.
1.1: Identify Points, Lines, & Planes
Objectives:
1. To learn the
terminology and
notation of the basic
building blocks of
geometry
Assignment:
• P. 5-8: 1, 5-7, 10-15,
23, 25, 39, 43, 47, 48
• Challenge Problems