# 1 3 Collinearity Betweenness Assumptions

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"1 3 Collinearity Betweenness Assumptions"

Collinearity,
Betweenness, &
Assumptions
Geometry 1.3
Collinear Points:
Points on the same line.

A    B      C
A, B, and C are COLLINEAR
points.
Non-Collinear Points:
Points not on the same line.

A, B, and C are Non-COLLINEAR
B       points.

A
C
Betweenness:
Points must lie on the same line
and AB + BC = AC.
Y

A        B           C                 Z
“B is between A and C”
X
Symbols: A-B-C           “Y is not between X and Z”
because the points are not
on the same line.
Triangle Inequality:
The sum of two sides of a triangle
must always be greater than the
third side.

3
B
8
AB = 3
BC = 8
AC = 11
}  3
Triangle can’t exist!

8
A               C      A          B           C
Triangle Inequality:
The sum of two sides of a triangle
must always be greater than the
third side.
5+7>x
5            7
12 > x
AND
5+x>7
X
x>2
AND           So, 2 < x < 12
7+x>5
x < -2
Assumptions From A Diagram.

Can Assume:
1.   Straight Lines and Angles

2.   Collinearity of Points

3.   Betweenness of Points

4.   Relative Position of Points
Assumptions From A Diagram.

Can Not Assume:
1.   Right Angles

2.   Congruent Segments

3.   Congruent Angles

4.   Size of An Angle

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