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POINTS, LINES, AND PLANES
Agenda:
• Warmup
• Notes/practice
• Quiz Thursday
• Unit 2 Test Wednesday 2/18
WARMUP
• (10, -4) AND (6, 0)
– FIND THE DISTANCE BETWEEN THE 2
POINTS.
– FIND THE SLOPE BETWEEN THESE 2
POINTS.
– FIND THE MIDPOINT.
Geometry: the study of points, lines
and planes as they exist in space.
These building blocks for Geometry are
accepted as intuitive ideas and are not defined.
Instead, they are described by their
characteristics and are also used in the
definitions of other terms. Approximate
examples can be seen in our every day lives.
Point – the simplest figure in geometry.
A point has no size and no dimension;
it represents one position in space.
Notation: Points are named by capital letters.
Example: Points A and B
A
B
A series of points can create a line. A line
extends in two directions without ending. A line
has only one dimension.
Notation: Lines can be denoted by using two points
that lie on the line or by using a lower case letter.
B
AB or BA
A
Line m
m
A plane can be visualized by looking at the floor or a
wall. It is a two dimensional figure that extends in
both dimensions forever and has no thickness. There
are no edges to a plane.
Notation: A plane is either named by one capital
letter (like a point!) or by at least three points (but
no more than four points) that lie in the plane.
B
D
Plane M
C
A
Plane ABC
or Plane ABCD
Where have you seen points, lines, and
planes before in math class?
The Coordinate Plane
Plotting Points.
Ex. (-2, 4)
Graphing Lines in
slope-intercept
form. Ex. y = 2x + 2
Space is the set of all points. Space has three
dimensions.
Collinear Points are points that lie on the
same line.
Are A and B
E
collinear points?
A
Yes!! In fact any
C
two points are
D
B
A, C, and D are collinear points.
B, C, and D are noncollinear points.
collinear. We
can always draw
exactly one line
between two
given points.
Coplanar Points are points that lie on the
same plane.
K
A
B
C
D
A, B, C, and D are
coplanar points.
G
J
H
K, J, G, and H are
noncoplanar points.
The intersection
of two figures is
the set of points
that are in both
figures.
The symbol for
“to intersect” is

If two lines
If two planes
intersect, then they intersect, then they
intersect at a point. intersect at a line.
B
q
r
line q  line r at point B.
M
p
N
plane M  plane N at line p.
Check for Understanding: CW
Textbook (pages 17-18) Exercises
pg. 17 #’s (3-8, 19-26) all
Intersection Examples:
G
E
F
D
H
A
C
B
1. Plane GEDF  Plane DFBC at DF.
2. Plane EDBA  Plane GEAH at EA.
3. DB  DF at Point D.
4. EF  EA at Point E.