Download Collinear

Warm Up
1.
70
2.
Use a ruler to draw a large triangle. Measure the angles of the
triangle. Make a conclusion about the sum of the measure of
the angles of a triangle.
1.3 Collinearity, Betweeness, and Assumptions
Collinear: points on the same line
A
B
Points ABC are collinear
C
Non-collinear: points that do not lie on
the same line
B
A
C
You can connect AB, AC, or
BC, but ABC does not form a
line.
Betweeness of Points:
To have betweeness of points, all points must
be on the same line.
Z
Y
X
Z is between Y and X
Y
Z
X
X is not “between” Y and Z
Triangle Inequality:
For any three points, only two possibilities:
1. Collinear: all points are on the same line.
(2 Distances add up to the third distance)
2. Noncollinear: 3 points determine a
triangle
Triangle Inequality: the sum of two sides is
always greater than the third side.
Why is this? Let’s take a ruler and measure
to see if this is true!!!
Assumptions from diagrams:
Can assume:
1. Straight lines
2. Straight angles
3. Collinear points
4. Betweenness of points
5. Relative position of points
Can’t Assume!
1.Right angles
2.Congruent segments
3.Congruent angles
4.Relative size of angles
5.Relative size of segments
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
Example:
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