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1.3 Points, Lines, and Planes
You will learn to identify and draw models of points,
lines, andplanes, and determine their
characteristics.
You will learn to identify and draw models of points,
lines, andplanes, and determine their
characteristics.Pardekooper
Lets start with some Lets start with some common terms.common terms.
• Point:Point: – a concept used to define a concept used to define
an exact location in spacean exact location in space
Pardekooper
- a point has - a point has no sizeno size
- named using capital letters- named using capital letters
Lets start with some Lets start with some common terms.common terms.
• Line:Line:– an ideal zero-width, an ideal zero-width,
infinitely long, perfectly infinitely long, perfectly straight curvestraight curve
Pardekooper
- made up of an - made up of an infiniteinfinite numbernumber of points. of points.
Let’s try a problem.
R
T
m S
Name two points on line m.
Possible answers:
point R and point S point R and point T point S and point T
Give three names for the line.
Possible answers:
NOTE: Any two points on the line or the script letter can be used to name it.
Here’s another problem.
R
T
m S
RS, RT, ST or line m
Lets start with some Lets start with some common terms.common terms.
• Collinear pointsCollinear points::– three or more three or more pointspoints
that lie in a straight linethat lie in a straight line
Pardekooper
R
TS
U
V
Name three points that are collinear.
Possible answers:
points R, S, and point T points U, S, and point V
Just one more problem
• Plane:Plane: –a two-dimensional
surface that is perfectly flat. {three non-collinear points determine a plane}
Lets start with some Lets start with some common terms.common terms.
Pardekooper
Coplanar:Coplanar:– Geometric objects lying in Geometric objects lying in
a common plane usually a a common plane usually a point and a line.point and a line.
Lets start with some Lets start with some common terms.common terms.
Pardekooper
How about thoseHow about thosePostulatesPostulates
Pardekooper
• 1-1:1-1: –Given two points, there
is exactly one line that goes through the points.
How about thoseHow about thosePostulatesPostulates
Pardekooper
• 1-21-2–Two lines intersect in
exactly one point
How about thoseHow about thosePostulatesPostulates
Pardekooper
• 1-31-3–Two planes intersect in
exactly one line
How about thoseHow about thosePostulatesPostulates
Pardekooper
• 1-4:1-4: – Given three non-colinear
points, there is exactly one plane that goes through the points.
--A plane can be named with a single uppercase script letter or by three noncollinear points.
M
AAAA
BBBB
CCCC
DDDD
EEEE
Name three points that are coplanar.
Answers (may be others)
A, B, & C or A, D, & E
A few more problems
AAAA
BBBB
CCCC
DDDD
EEEE
Name three points that are
noncoplanar.
Answers (may be others)
D, A, & B B, A, & ED, A, & C C, A, & E
A few more problems
AAAA
BBBB
CCCC
DDDD
EEEE
Name a point that is in both planes.
A
A few more problems
Assignment
Pardekooper
Are the following sets of points coplanar ?1. AB and C 2. B and F
3. EB and A 4. F in plane Q
1.3 Points, Lines and PlanesGeometry
A B
C
D
E
Q
F
Find the intersection of the following lines and planes in the figure at the right
5. GK and LG 6. DB and FC
7. F, A, B, and C 8. FB and BD
G
H
K J
L
M
P
N
Refer to the diagram at the right.
9. What is the intersection of plane P and Q ?
10. Are A and C collinear ?
11. Are planes P and Q coplanar?
Q
P
A
BC
D
