Warm Up
 Set a personal goal for the semester
 List 3 terms and definitions that you may already
know from previous Geometry units in your other
classes
Solve each equation
(leave all non-integer
answers as reduced fractions).
1. 5x – 3 = 18
x = 21/5
2. 4(x – 1) + 2 = 15
x = 17/4
3. 8x + 9 = 14x – 3
x=2
4. 12x + 5 = 18x
x = 5/6
5. 3(2x + 1) = 5(x + 7)
x = 32
Points, Lines
& Planes
• Objectives:
– I will learn about the building blocks of geometry – the point, line, and
plane
– I will learn definitions and notation of basic geometric figures
• Essential Questions:
– Why are points, lines, and planes the undefined terms of
Euclidean geometry?
– Why is it important to use a conventional method for naming and
notating points, lines, segments, rays, angles, and planes?
– How are these figures notated?
Definition – A point represents a single
location in space.
It has no size and NO DIMENSION.
It represents the simplest form of geometry.
Notation: Points are
named by capital letters.
Example: Points A and B
A
B
Definition - A series of points can create a line.
A line extends in two directions without endpoints.
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
Given any two points, you
can draw exactly one
line. You can draw an
infinite amount of lines
through one point.
AB or BA
A
Line m
m
Definition - A two dimensional figure that extends
in both dimensions forever and has no thickness.
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
x
y
z
Space is the set of
all points. Space
has three
dimensions.
Collinear Points are points that lie on the
same line.
E
A
C
D
B
A, C, and D are collinear points.
B, C, and D are noncollinear points.
Are A and B collinear points?
E
A
C
D
B
Yes!! In fact any two points are
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.
If two lines
intersect, then
they intersect
at a point.
Where does AB
intersect AE?
Point A or A
A
B
D
C
E
H
F
G
If two planes
intersect, then
they intersect
at a line.
A
B
D
C
E
G
H
Where does ABCD intersect
BCGF?
F
BC
True/False
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Line XY intersects plane M at point O
Plane M intersects XY in more than one point
T, O and R are collinear
X, O and Y are collinear
R, O, S and W are coplanar
R, S, T and X are coplanar
R, X, O and Y are coplanar
Does a plane have edges
Can a given point be in 2 lines? In 10 lines?
Can a given line be in 2 planes? In 10 planes?
X
M
S
T
O
R
W
Y
Complete this activity alone
and then compare with seat
partner
Name a 4th point in the same plane
11. A, B, C, ____
C
D
A
B
12. E, F, H, ____
H
13. D, C, H, ____
14. A, D, E, ____
E
15. B, E, F, ____
16. B, G, C, ____
17. Are there any points in CG besides C and G
18. Are there more than 4 points in plane ABCD
19. Name the intersection of planes ABFE and BCGF
20. Name 2 planes that do not intersect
G
F
Postulates!
• Statements/Rules that are accepted
without proof
• Postulate 5: A line contains at least two
points; a plane contains at least three
points not all in one line; space contains at
least four points not all in one plane
Through any two points there is
exactly one line
Through any three points there is at
least one plane. Through any three
non-collinear points, there is exactly
one plane.
If two points are in a plane, then the
line that contains those points is also in
that plane.
All collinear points are also coplanar.
However, coplanar points are not
necessarily collinear.
D
C
A
B
Through a line and a point not on that
line, there is exactly one plane.
If two lines intersect then exactly one
plane contains both of them.
Connect Term with Definition
Point
Set of all points in 2 figures
Line
Points in the same line
Plane
Set of all points
Collinear
Location in space
Coplanar
Figure that goes to infinity in 2 directions
Space
Flat surface infinite in all directions
Intersection
Points in the same plane