In this item, we are given that the rays are opposite. We consider each of the choices and justify why each is true or false in order to answer this item.
1. A, B, C are collinear
For points, collinear means they lie on the same line. For rays to be opposite, they should be in the same line making a 180° or a straight line with each other. Hence, this statement is TRUE.
2. A, B, C are coplanar
Coplanar means the points lie in the same plane. For these rays to be opposite and collinear as justified in 1, the points should lie in the same plane. This is TRUE.
3. AB = AC
This is not entirely true. The ray is a geometric figure with one enpoint and the other end extends infinitely. Therefore, there is no definite measure of the rays. Hence, this is FALSE.
4. A is in betweeen B and C
In the names of the rays, it is known that A appears for both AB and AC. This means that point A is shared and must be between points B and C. This statement is TRUE.
Therefore, the only false statement is number 3.
