Why do chairs sometimes wobble?
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Have you ever noticed that a four legged
chair sometimes wobbles, but a threelegged stool never wobbles?
Points, Lines and Planes
Section 1.12
Points
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An undefined term in geometry. (explained using examples
and descriptions.)
They have no size
B
How do you represent a point?
By using a dot
A
XC
B
How do you label a Point?
With a capital letter
Never use the same letter on two different points.
A point has neither shape nor size.
What are some examples of points?
Stars, Corner of the room
HAS NO LENGTH ,WIDTH, or AREA!
Draw points and label on
vocabulary sheet.
Lines
A basic undefined term of geometry.
A line is made up of points and has
no thickness or width.
In a figure, a line is shown with an
arrowhead at each end.
Lines are usually named by lowercase
script letters or by writing capital
letters for two points on the line,
with a double arrow over the pair of
letters.
Draw and label lines on vocabulary
sheet.
Examples of lines:
Phone lines strung between poles, spider
webs, sun beams.
Collinear Points: (draw on vocab sheet)
Points that lie on the same line.
Non-collinear Points:(add to vocab sheet)
Points that do not fall on the same line.
Planes
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Undefined term in geometry
Are thought of as flat surfaces that extend indefinitely in
all directions and have no thickness.
There are two ways to label planes:
1. Using a capital script letter – S
2. Using any three non-collinear points –
XYZ, XZY, YXZ, YZX, ZXY, ZYX
Two planes intersect in one line.
Draw and label planes on
vocabulary sheet.
Planes are unbounded
flat surfaces with no
edges or corners.
Coplanar:
Points that lie on the same plane.
Non-coplanar: (add to vocabulary sheet)
Points that do not lie on the same line.
What are some examples of planes
in the classroom?
Top of desk
 Wall
 Chalkboard
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Remember: A plane extends indefinitely
in all directions. The examples above do
not completely satisfy the description.
Activity
1.
2.
3.
4.
5.
Each student gets two cards
Label one Q and one R.
Hold the two card together and place a
slit halfway through both cards.
Hold cards so that the slits matchup and
slide them together. (Tape cards
together)
Where the cards meet models a line.
Draw the line and label two points C
and D on the line.
Activity Cont.
1.
2.
3.
4.
Draw point F on your model so that it
lies in Q but not R. Can F lie on line
DC?
Draw point G so that is lies in R but not
Q. Can G lie on line DC?
If point H lies in both Q and R where
would it lie? Draw it on your model.
Draw a sketch of your model on your
paper. Label each part appropriately.
102nd floor
82nd floor
Which tennis balls are coplanar?
Example 1: Use the figure to name each of the following.
n
Q
V
T
m
P
S
1.
2.
3.
4.
5.
R
Give two other names for PQ .
Give two other names for Plane R.
Name 3 collinear points.
Name 4 points that are coplanar.
Name a point that is not coplanar with points Q,S,and T.
Example 2: Draw and label a figure for each relationship.
D
B
C
P
E
A
R
Space
Is a boundless three dimensional set of all
points. Space can contain lines and planes.
Example 3
1.
2.
3.
4.
How many Planes are there?
Name three points that are collinear.
Are points A, B, C, & D coplanar?
Explain.
CD
AB
At what point do
and
intersect?
Example 4
1.
2.
3.
4.
How any planes are there?
Name three collinear points.
AB
EF
Are points G, A, B, & F coplanar? Explain
At what point do
and
intersect?
Example 5
Points, Lines, and Planes
As you look at the cube, the front face is on which plane?
The back face is on which plane?
The left face is on which plane?
The back and left faces of the cube intersect at?
Planes HGC and AED intersect vertically at?
What is the intersection of plane HGC and plane AED?
Example 6
Name each shaded plane
.
1-2
Line Segment
A measurable part of a
line that consists of two
points, called
endpoints, and all of the
points between them.
Ray
It has one endpoint and
extends indefinitely in
one direction.
is a ray if it is the set of
points consisting of and
all points S for which Q
is between P and S
Opposite Ray
Two rays that share the
same endpoint and form
a line
Example 7
Points, Lines, and Planes
Use the diagram at right.
1. Name three collinear points.
D, J, and H
2. Name two different planes that contain points C and G.
planes BCGF and CGHD
3. Name the intersection of plane AED and plane HEG.
HE
4. How many planes contain the points A, F, and H?
1
5. Show that this conjecture is false by finding one counterexample:
Two planes always intersect in exactly one line.
Sample: Planes AEHD and BFGC never intersect.
Example 8
Points, Lines, and Planes
Shade the plane that
contains X, Y, and Z.
Points X, Y, and Z are the vertices of one of the
four triangular faces of the pyramid. To shade
the plane, shade the interior of the triangle
formed by X, Y, and Z.
Why do chairs sometimes wobble?

Have you ever noticed that a four legged
chair sometimes wobbles, but a three
legged stool never wobbles? This is an
example of points and how they lie in a
plane. Explain.