Section 13: Points, Lines, and Planes

1
Section 1-3 Points, Lines, and Planes
Goal Be able to understand basic terms and
postulates of geometry.
Warm up Solve the system of equations. y
2x 4 4x y 10
Graphing
Substitution
Elimination
4x (2x 4) 10 2x 4 10
2x 6 x 3
-2x y - 4 4x y 10
2x 6 x 3
y 2(3) 4 y 2
y 2(3) 4 y 2
(3, 2)
(3, 2)
(3, 2)
2
point - ______________________
______________________
has no size, represented by a dot,
named by a capital letter
A
______________________________ ___________________
___________
all geometric figures consist of points
space - ______________________
a boundless, 3-D set of all points
3
line - ________________________
________________________
series of points that extends in
two opposite directions without end
m
Q
PQ
line PQ
P
line m
QP
Points that lie in the same line are
____________________.
collinear points
4
In the figure below, name 3 points that are
collinear and 3 points that are not collinear
(noncollinear).
X
Z
W
Y
Y, Z, and W are collinear
X, Y, and Z are not collinear
X, W, and Z are not collinear
5
Plot __________________________________
__________________________________
A(0, -4), B (2, 2), and C(3, 5) on a coordinate
plane.
C
B
A
___________________________________________
__ _______________________________________
______
What are your observations?
Points A, B, and C are
collinear.
6
plane - _______________________
_______________________
_______________________
_______________________
a flat surface that has no thickness
contains many lines
and extends
infinitely far in the direction of its
lines.
R
B
C
A
Plane R
Plane ABC
A, B, C are noncollinear points
Points and lines in the same plane are
___________.
coplanar
7
1. Name two different planes that contain points
C and G.
C
G
B
F
D
H
A
E
J
plane BCG, plane DCG
2. Name the intersection of plane AED and plane
HEG.
HE
3. How many planes contain the points A, F, and
H?
(3 noncollinear points)
1
8
postulate - _____________________
_____________________
or axiom an accepted
statement of fact
Postulate 1-1_________________________ ___________
___________________
Through any two points,there
is exactly one line.
m
B
A
9
Postulate 1-2 ________________________ ___________
___________________
If two lines intersect,
then they
intersect in exactly one point.
Postulate 1-3 ________________________ ___________
___________________
If two planes intersect,
then they
intersect in exactly one line.
P
Plane PQR and Plane QRS intersect at QR
S
Q
R
10
Postulate 1-4 ___________________________ ________
______________________
Through any 3 noncollinear points
there is exactly one plane.
B
A
C
Plane ABC