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 - ______________________ ______________________
Location with no size, represented by a
small dot, named by a capital letter A
______________________________
a geometric figure consist of
a set 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 (PQ are collinear)

4. X, Y, and Z are not collinear X, W, and Z are not collinear
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
Why are arrowheads on the lines?
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. a flat surface that has no thickness;
plane - _______________________ _______________________ _______________________ _______________________
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.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)

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

11. What is the difference between a postulate and a conjecture?