Chapter 1
Tools Of Geometry
Drill
a) 1, 3, 5, 7, 9, __, __
b) 2, 5, 8, 11, 14, __, __
c) -3, -6, -10, -15, ___
d)
,
,
, ___
1.1
Using Patterns and
Inductive Reasoning
Notes
Inductive Reasoning: Allows
you to reach conclusions
based on a pattern of specific
examples.
Ex: Someone eating the same
breakfast everyday.
Conjecture: A conclusion
reached using inductive
reasoning.
Example: Make a conjecture about
the shapes.
Points Regions
2
3
4
5
6
2
Use Inductive Reasoning To
find the sum of the first 20 odd
numbers
1
1+3
1+3+5
1+3+5+7
1+3+5+7+9
= 1
= 4
= 9
= 16
= 25
1.2
Points, Lines, and Planes
Drill
Find the next number in the
sequence:
a) -3, -1, 1, 3, __, __
b)1, 4, 2, 5, 0, __, __
Name three things in the real
world that represent a line, a
point and an angle.
Notes(Vocab)
Points: have no size, often
represented with dots, and
named with a capital letter.
C
A
B
Lines: have no thickness, and
extend infinitely in two
directions. Named with two
points, or a cursive letter.
l
Y
X
• Collinear: points that are lying
in the same line.
A
B
C
• Non-Collinear: Not lying in
the same line.
C
A
B
Planes: Extend infinitely in all
directions. It is flat and has no
thickness. There are two ways to
name a plane.
• To Name a plane you need 3 noncollinear points.
Coplanar: Points and lines that are
in the same Plane.
Postulates: an accepted statement
or fact.
*The intersection of two lines is a
______.
point
*The intersection of two planes is a
______.
line
*Through any two points lies exactly
one ______.
line
*Through any three non-collinear
points there is exactly one ______.
plane
A
C
B
D
E
F
I
H
G
Drill
a) Two planes intersect to make a
___.
b) Two lines intersect to make a ___.
c) How many different ways can
you name this line?
A
B
C
D
1.3
Segments, Rays, Parallel
Lines and Planes
Segments: Are parts of lines,
they have two endpoints,
and are named by using the
two endpoints.
• Rays: is a “half-line”. It has
one endpoint and extends
infinitely in one direction.
• Opposite Rays: share the
same endpoint and go in
opposite directions.
Parallel Lines: are lines that are
in the same plane and do not
intersect.
• Parallel Planes: Two planes
that never intersect.
• Skew Lines: Lines that do not
intersect but are not parallel,
because they are in different
planes.
A
C
B
D
E
F
I
H
G