The Segment Addition Postulate involves the addition of two segments with a common endpoint. Which conditions regarding the endpoints must be met?

Question

The Segment Addition Postulate involves the addition of two segments with a common endpoint. Which conditions regarding the endpoints must be met? Check all that apply. they are collinear 

they are coplanar

they are noncollinear 

the points are randomly placed on a plane

one point is between the other two​

Answer 1

Here is an example of three points (A, B, C) to which the Segment Addition Postulate applies:

A--------B--------------C

The two segments are AB and BC. The Segment Addition Postulate is AB + BC = AC.

1. As you can see, the three points (A, B, C) are colinear - that is, they lie on the same line
2. Since any three points define a plane, colinear points are also co-planar. However, since they are colinear, there are an infinite number of planes that contain the three points
3. The points cannot be randomly placed on a plane because random points may not be colinear
4. If the points are colinear, they cannot be non-colinear
5. Finally, if the three points are colinear, one of them must lie between the other two. In the above example, B lies between A and C