Section 1.3: Collinearity, Betweenness, and Assumptions

Points that lie on the same line are called collinear.

Points that do not lie on the same line are called noncollinear.

.

When you say a point is between two other points,  the points must be collinear.

On the left, points A, B, and C are collinear;

point B is between points A and C. 

On the right, A, B, and C are not collinear;

so point B is not between points A and C...

.

.

There are some things that you can and can't assume from diagrams.

.

You should assume:

straight lines and angles... if a line looks straight, it is

the collinearity/ betweenness of points... if they look collinear, they are

the relative positions of points... if A appears to the right of B, then it is

.

You should not assume:

right angles... if it looks like a right angle, it doesn't mean it is

congruent segments/angles... if they look the same, it doesn't mean they are

relative sizes of segments/ angles... if one looks bigger, it doesn't mean it is 

.

.

Triangle Inequality

 Not just any three line segments can make a triangle.

.

On the left,  AB + BC = AC so it ends up being a straight line, not a triangle.

.

On the right, two of the segments cannot come to a point at the top because they are too short relative to the base.

.

SO... the sides of your triangle must fit the form

AB+BC>AC

(AB+AC>BC

AC+BC>AB)

.

That's all we learned today

for Enjoyment and Challenge,  this is Olivia Miller