Line Segment
In short: A line segment is a straight, bounded piece cut from a line by two endpoints, which gives it a fixed length you can measure with a ruler.
GeometryGeometryG-CO.A.1
What is Line Segment?
Take two points on a straight path and keep only what lies between them: that piece is a line segment. It has two endpoints and one fixed length. It is written \(\overline{AB}\), while its length is written \(AB\).
The segment addition postulate says that if point \(M\) lies between \(P\) and \(Q\), then \(PM + MQ = PQ\). Two segments with equal lengths are congruent, written \(\overline{AB} \cong \overline{CD}\).
How to spot it
- A figure shows a line segment as a straight piece with a dot at each end, like a fence rail, a ladder or a polygon side.
- The statement places a point between two others and sets up pieces whose lengths add up to a total.
- You are asked for a distance, a length in inches or feet, or whether two sides are congruent.
- The notation has a bar over two letters, as in \(\overline{XY}\), with no arrowheads.
The method
- Name the two endpoints and write the piece with a bar over the letters: \(\overline{PQ}\).
- If a point \(M\) sits between them, write the addition equation \(PM + MQ = PQ\).
- Replace each part by its given expression and solve the equation for the unknown.
- Substitute back to get every length, and confirm the parts really add up to the whole.
Line Segment: solved example
Problem
A 36-inch shelf board \(\overline{PQ}\) has a drilled hole at \(M\) between its ends, with \(PM = 2x + 3\) and \(MQ = 5x – 9\). Find \(x\) and both lengths.
Solution
By segment addition, \((2x + 3) + (5x – 9) = 36\), so \(7x – 6 = 36\) and \(7x = 42\), giving \(x = 6\).
Then \(PM = 2(6) + 3 = 15\) and \(MQ = 5(6) – 9 = 21\). Check: \(15 + 21 = 36\). The pieces measure 15 inches and 21 inches.
Try it
Question 1
Point \(Z\) lies between \(X\) and \(Y\). If \(XY = 8.4\) cm and \(XZ = 3.9\) cm, find \(ZY\).
Show the answer
\(ZY = 8.4 – 3.9 = 4.5\) cm.
Question 2
On a number line, one segment runs from \(-7\) to \(11\) and another from \(2\) to \(20\). Are they congruent?
Show the answer
The lengths are \(11 – (-7) = 18\) and \(20 – 2 = 18\). They match, so the two are congruent.
Line Segment vs. Ray
A ray begins at one endpoint and keeps going forever, so it has no length to measure. A segment stops at both ends. The ray \(\overrightarrow{AB}\) passes through B and continues; the piece \(\overline{AB}\) ends at B, and only the latter can be 36 inches long.
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Whole dictionary: A–Z · Geometry · Geometry