Segments, Rays & the Segment Addition Postulate

Pieces and the whole

First, a note on notation: $\overline{AB}$ with a bar names the segment itself, while $AB$ with no bar means its length — a number. The Segment Addition Postulate is a statement about lengths, so it is written without bars: $AB + BC = AC$.

The point in the middle of the betweenness statement is the one splitting the segment. If $B$ is between $A$ and $C$, then $AB$ and $BC$ are the pieces and $AC$ is the whole. Given both pieces, add to get the whole. Given the whole and one piece, subtract to get the other piece.

When the pieces are expressions

Often the pieces are given as expressions like $2x + 1$ and $x + 4$ with a number for the whole. Set up the same equation — pieces on one side, whole on the other — then combine like terms and solve for $x$.

Read the question twice at the end. Some problems ask for $x$, but many ask for a length like $BC$, which means one more step: substitute your $x$ back into the expression for that piece.

The classic trap

The most common mistake is adding two numbers that are not both pieces. If a problem gives $AB = 25$ and $AC = 40$, then $AC$ is the whole — adding gives a wrong answer of $65$. Sketch the segment, label the three points in order, and mark each given length on the sketch before you compute. The picture makes the whole and the pieces obvious.

Worked examples

Try one yourself

Common questions