Key takeaway: A line segment is a straight, bounded stretch between two endpoints, which makes it the one linear figure whose size can be measured with a ruler and recorded as a length.
Grade 10 – GeometryG-CO.A.1Geometry and Measurement
Definition of Line Segment
Cut a straight line at two places and keep the middle: that is a line segment. The cut points are its endpoints, and the piece includes both of them plus everything lying between.
Since the stretch is bounded, you can lay a ruler along it. The distance from one endpoint to the other is the length of the segment. When two segments have the same length they are congruent. A point that sits exactly halfway between the endpoints is the midpoint.
Formula and notation
Write a segment with a bar over its endpoints, \(\overline{PQ}\). Its length has no bar:
\[ PQ = 9.5 \text{ cm} \]
If \(R\) lies between \(P\) and \(Q\), the Segment Addition Postulate says \(PR + RQ = PQ\). Congruent segments are written \(\overline{AB} \cong \overline{CD}\).
Key facts
- Counting endpoints separates the figures: two for a segment, one for a ray, none for a line.
- Congruent segments have the same length, though they may point in different directions.
- The midpoint divides a segment into two segments of equal length.
- Length is a number with units, while the segment itself is the geometric figure.
Line Segment example
Point \(M\) lies on \(\overline{AB}\) between \(A\) and \(B\). If \(AM = 3x + 4\), \(MB = 5x – 6\) and \(AB = 46\), find \(x\) and the length \(AM\).
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Segment Addition: \(AM + MB = AB\), so \((3x + 4) + (5x – 6) = 46\).
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Combine like terms: \(8x – 2 = 46\), so \(8x = 48\) and \(x = 6\).
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Then \(AM = 3(6) + 4 = 22\) and \(MB = 5(6) – 6 = 24\); check \(22 + 24 = 46\).
\(x = 6\) and \(AM = 22\) units.
Common mistake
Watch out
Elena says a line segment goes on forever, so \(\overline{AB}\) has no length that can be measured.
Why it is wrong
She is describing a line. A segment stops at both endpoints \(A\) and \(B\), so it has a definite length. If the figure goes on forever in both directions it is \(\overleftrightarrow{AB}\), and if it goes on in one direction only it is a ray.
Related terms and lessons
Browse the glossary: A–Z list · Geometry vocabulary · Geometry and Measurement