Transcript Lesson 1.3 Powerpoint

Lesson 1.3
Collinearity, Betweenness, and
Assumptions
Objective:
Recognize collinear, and non-collinear points, recognize
when a point is between two others, recognize that each side
of a triangle is shorter than the sum of the other two sides,
and correctly interpret geometric diagrams
Definitions…
Def. Points that lie on the same line are called
collinear.
Def. Points that do not lie on the same line are
called noncollinear.
P
U
A
H
S
N
Collinear
Noncollinear
Example #1
Name as many sets of points as you
can that are collinear and
noncollinear
O
R
S
M
X
Y
P
T
Definitions…
In order for us to say that a point is between two
other points, all three points MUST be collinear.
U
A
P
H
S
N
A is between N and U
P is NOT between H and S
Triangle Inequality
For any 3 points there are only 2 possibilities:
1. They are collinear (one point is between the other
two and two of the distances add up to the 3rd)
A
C
B 5.5
12.5
18
2. They are noncollinear (the 3 points determine a
B
triangle)
14
11
A
24
C
Triangle Inequality
Notice in this triangle, 14 + 11 > 24.
This is extra super important!
“The sum of the lengths of any 2 sides of a triangle is
always greater than the length of the third”
B
14
11
A
24
C
Assumptions
When given a diagram, sometimes we need to
assume certain information, but you know what they
say about assuming….
There are do’s and don’ts!
You should Assume
*Straight lines and angles
*Collinearity of points
*Betweenness of points
*Relative positions of points
You should NOT
Assume
*Right angles
*Congruent segments
*Congruent angles
*Relative sizes of segments
and angles
Homework
Lesson 1.3 Worksheet