Segments, rays and length
A line goes on forever both ways. What do you get when you cut a piece off it, and how do lengths behave along it?
Where you are 4 inside
What this area is about
A line never ends, so it has no length. Stop it at one point and you get a ray, \overrightarrow{AB}, which starts at A and runs on forever through B. Stop it at two points and you get a segment, \overline{AB}, which does have a length, written AB with no bar. This area is about that length: how to find it, when two segments match, and how lengths add along one line.
How these fit together
Measuring. Distance on a number line is a procedure: it finds a length from the coordinates a and b of the two ends, AB = |b - a|, even when they are negative.
Comparing and adding. Segment length, addition and congruence holds a definition and a rule. Two segments with the same length are congruent, \overline{AB} \cong \overline{CD}. The segment addition postulate says that when B is between A and C, AB + BC = AC.
The middle. Midpoints and segment bisectors: the midpoint splits a segment into two congruent halves, and any line, ray or segment through it is a segment bisector. The perpendicular bisector of a segment is the line through its midpoint at a right angle to it.
A path through it
Distance on a number line and segment length, addition and congruence can come in either order. Then midpoints and segment bisectors, then the perpendicular bisector, each built on the one before.
Finish here and you can measure, compare and split lengths. That is where medians of a triangle, compass and straightedge constructions and distances on a coordinate grid start.