1. Collinearity, Betweeness, and Assumptions
Lesson 1.3

2. Collinear: points on the same line
Points ABC are collinear A B C
Non-collinear: points that do not lie on the same line B A
You can connect AB, AC, or BC, but ABC does not form a line. C

3. Betweeness of Points:
To have betweeness of points, all points must be on the same line. Y Z X
Z is between Y and X Y Z X
X is not “between” Y and Z

4. Triangle Inequality Two possibilities with 3 points
Collinear: all points are on the same line.
Triangle : makes a triangle.
Triangle Inequality
The sum of two side lengths is always greater than the third side.

5. Assumptions from diagrams:
Can assume:
Straight lines
Straight angles
Collinear points
Betweenness of points
Relative position of points

6. Can’t Assume!
Right angles
Congruent segments
Congruent angles
Relative size of angles
Relative size of segments

7. Example: B D A C E Assume: AD and BE straight lines
C, D, E non-collinear
C is between B and E
E is to the right of A

8. B D A C
Can’t Assume:
<BAC is a right angle
CD = DE
<B = <E
<CDE is obtuse
BC is longer than CE E