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
4x – (2x – 4) = 10
2x + 4 = 10
2x = 6
x=3
y = 2(3) – 4
y=2
(3, 2)
(3, 2)
Elimination
-2x + y = - 4
4x – y = 10
2x = 6
x=3
y = 2(3) – 4
y=2
(3, 2)
Location with no size, represented by a
point - ______________________
small dot, named by a capital letter
______________________
A
______________________________
a
geometric figure consist of
______________________________
a
set of points
a boundless, 3-D set of all points
space - ______________________
series of points that extends in
line - ________________________
________________________
two opposite directions without end
Q
P
m
PQ
line PQ
QP
line m
Points that lie in the same line are
_______________.
collinear points
(PQ are collinear)
In the figure below, name 3 points that are
collinear and 3 points that are not collinear
(noncollinear).
X
Y
Z
Y, Z, and W are collinear
X, Y, and Z are not collinear
X, W, and Z are not collinear
W
Why are
arrowheads
on the lines?
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.
_____________________________________________
plane - _______________________
a flat surface that has no thickness;
_______________________
contains many lines and extends
_______________________
infinitely far in the direction of its
lines.
_______________________
R
B
A
Plane R
Plane ABC
C
*A, B, C are
noncollinear points
Points and lines in the same plane are ___________.
coplanar
C
G
B
F
D
H
A
E
J
1. Name two different planes that contain points C and G.
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?
1 (3 noncollinear points)
or axiom; an accepted
postulate - _____________________
statement of fact
_____________________
Postulate 1-1_________________________
Through any two points,there
is exactly one line.
______________________________
B
A
m
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
S
Q
R
Plane PQR and
Plane QRS
intersect at QR
Postulate 1-4 Through
___________________________
any 3 noncollinear points
there
is exactly one plane.
______________________________
B
A
C
Plane ABC
What is the difference
between a postulate and a
conjecture?