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?
Geometry 1.1 Points, Lines and Planes
August 15,
2016
What Will You Learn?
• Understand and use the basic
undefined terms and defined terms
of geometry.
• Sketch the intersection of lines and
planes.
• Solve real-life problems involving lines
and planes.
Geometry 1.1 Points, Lines and Planes
August 15,
2016
Where Do We Start?
Geometry 1.1 Points, Lines and Planes
August 15,
2016
What are these terms?
Undefined Terms
Defined Terms
• Point
• Line
• Plane
•
•
•
•
•
•
Geometry 1.1 Points, Lines and Planes
Collinear Points
Coplanar Points
Line Segment
Ray
Opposite Rays
Coplanar
August 15,
2016
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:
Geometry 1.1 Points, Lines and Planes
August 15,
2016
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.
A
B
l
Geometry 1.1 Points, Lines and Planes
August 15,
2016
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:
A
line AB
B
l
line BA
line l
Geometry 1.1 Points, Lines and Planes
AB
BA
𝑙
August 15,
2016
3 Undefined Terms
Plane: A plane has two dimensions. It is a
flat surface with length and width but no
thickness.
M
A
B
Geometry 1.1 Points, Lines and Planes
C
August 15,
2016
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:
A
plane ABC
plane M
Geometry 1.1 Points, Lines and Planes
M
B
C
August 15,
2016
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:
Segment RS
RS
Segment SR
SR
Geometry 1.1 Points, Lines and Planes
R
S
endpoints
August 15,
2016
Definitions
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:
Ray MP or MP
M
P
Initial Point
The initial point is always first!
NOT Ray PM or PM!
August 15,
Geometry 1.1 Points, Lines and Planes
2016
Same Ray, Different Name
AB and AC
are the same
ray!
A
Geometry 1.1 Points, Lines and Planes
C
B
They have the
same initial
point, and B and
C are collinear.
August 15,
2016
Definitions
• Collinear: On the same line
F, Z, and P are collinear.
F
Z
P
• Coplanar: On the same plane
B, C, and M are coplanar.
Geometry 1.1 Points, Lines and Planes
B
C
M
August 15,
2016
Example 1
L
a. Name four coplanar points.
M
N
L, M, N, O
O
b. Name four points that are
P
not coplanar.
L, M, N, P or M, N, O, P or N, O, M, P
c. Name three collinear points.
L, N, O
Geometry 1.1 Points, Lines and Planes
August 15,
2016
Example 2
Draw three collinear points A, B, and C.
Draw point D which is not collinear with A,
B, and C. Draw 𝐴𝐵 and 𝐵𝐷.
D
A
Geometry 1.1 Points, Lines and Planes
B
C
August 15,
2016
Opposite Rays
A
C
B
Opposite Rays have the same endpoint and are collinear.
CA and CB are Opposite Rays
Geometry 1.1 Points, Lines and Planes
August 15,
2016
Are these Opposite Rays?
No! They
are not
collinear.
Geometry 1.1 Points, Lines and Planes
August 15,
2016
Example 3
Name two pairs of opposite rays.
E
F
Possible Answers:
G
H
FE , FG , GE , GH
FE , FH , GF , GH
Geometry 1.1 Points, Lines and Planes
August 15,
2016
Example 4
Sketch one plane with a line in the
plane that intersects a line not in the
Use the
plane.
dotted line
to indicate
this part of
the line is
behind the
plane.
Geometry 1.1 Points, Lines and Planes
August 15,
2016
Example 5
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.
Geometry 1.1 Points, Lines and Planes
August 15, 2016
Example 6
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.
Geometry 1.1 Points, Lines and Planes
August 15, 2016
Example 6
d. Name a point that is not collinear with
points A, C, and E.
e. Name two pairs of opposite rays.
Geometry 1.1 Points, Lines and Planes
August 15, 2016
Essential Question Revisited
What are the three undefined
terms and what is important
about these three objects?
Geometry 1.1 Points, Lines and Planes
August 15,
2016
Assignment
1.1 worksheet
Geometry 1.1 Points, Lines and Planes
August 15,
2016