Definition: A line segment is the part of a line between two endpoints, containing both endpoints and every point between them; its length is the distance between the endpoints.
What is a segment?
Unlike a line, which runs forever, a segment stops at two points. Write it as AB with a bar over the letters, and write its length as AB without a bar. Two segments are congruent when their lengths are equal.
What does the segment addition postulate say?
If B lies between A and C, then AB + BC = AC. This lets you set up equations for unknown lengths.
Example. Point Q lies between P and R, with PQ = 3x + 2, QR = 5x – 6, and PR = 40. Then (3x + 2) + (5x – 6) = 40, so 8x – 4 = 40 and x = 5.5. Therefore PQ = 18.5 and QR = 21.5, and 18.5 + 21.5 = 40 checks.
What errors occur?
Students apply the postulate when the three points are not on one line, or when B is not between the other two. Another slip is to treat a segment as having a direction; the segment AB and the segment BA are the same. Remember that the notation with a bar names the figure, while plain letters name a number.