Download Modeling points lines and planes.

Points
Undefined term
No length, width, or thickness
Named with a capital letter
Lines
Undefined term -- No thickness
Length that goes on forever in two
directions
A straight arrangement of points
Plane
Undefined Term
Has length, width W
but no thickness
Extends indefinitely
in all directions
Plane ABC
Plane W
The “building blocks of
geometry”:
• Ancient Greeks: “A point is that
which has no part.” “A line is
breadthless length”.
• Ancient Chinese: “The line is
divided into parts, and that part
which has no remaining part is a
point.”
• Not much help, huh?
A definition is a statement that
clarifies or explains the meaning of a
word or phrase.
• Unfortunately, we can’t define point,
line or plane w/out using words that
they themselves need defining, so…
• Point, line and plane are the 3
undefined terms of geometry, yet
they are the building blocks for all
geometry.
• IOW, using these three words, you
can define all other geometric
terms/figures.
Naming Lines
Intersecting Lines
Lines that share a point.
Y
n
m
Lines m and n intersect.
Point Y is the point of intersection.
Perpendicular Lines
Two lines that intersect to form a right
angle.
r
s
Lines r and s intersect to form a
right angle.
Parallel Lines
Lines in the same plane that do not
intersect.
k
j
Lines k an j are parallel.
k || j
Skew Lines
Lines that do not lie on the same
plane. (They do not intersect and
are not parallel.)
Collinear
Points that are on the same line.
A
B
Points A, B and C are
collinear.
C
Non-collinear
Points that are not on the same line.
A
B
Points A, B and C are non collinear.
C
Segment
Part of a line that has two
endpoints and contains all of the
points in between the two
C
endpoints.
AB
AB
B
A
AB
BC
AC
Ray
A part of a line consisting of one
point and all points on one side
of the line from that point.
C
B
A
BA CA CB
AB AC BC
Congruent
Two or more figures that have
the exact same size and shape.
Congruent symbol

Midpoint
A point that lies on the segment
and is equal distance from each
endpoint.
C
B
A
AB  BC
Space
The set of all points.
Coplanar Points
Points that lie on the same
plane.
Q
P
R
Points P, Q and R are coplanar.
Coplanar Lines
Lines that lie on the same plane.
x
y
Lines x and y are coplanar.
Non-Coplanar Points
Points that do not lie on the
same plane.
S
Q
P
R
Points P, Q, R and S are non-coplanar.
Postulates/Axiom
s
Statements that are accepted as
true.
Theorems
Statements that are proven to be
true.
Postulate
Through any 2 points there is
exactly one line.
B
A
m
Line m is the only line
containing both A and B
Postulate
Every line contains at least
two points.
p
B
A
Line p contains points A and B.
Postulate
If two lines intersect, their
intersection is a point.
n
P
m
Lines m and n intersect
at P.
Postulate
For any three noncollinear points,
there is exactly one plane
containing them.
B
Q
C
A
Points A, B, and C lie in Plane Q.
Postulate
Every plane contains at least
three noncollinear points.
Y
X
A
Z
Plane A contains points X, Y and Z.
Postulate
If two planes intersect, their
intersection is a line.
Z
k
W
Planes W and Z intersect in line k.
Postulate
If two lines intersect, then they
are coplanar.
m
n
Lines m and l lie in only one plane.
THE END