Line Segments: Definition, Measurement, Midpoints & Practice

A line segment is the part of a straight line between two endpoints, including those endpoints. It has a measurable length. To measure a drawn segment, align one endpoint with the ruler’s zero mark and read the scale at the other endpoint.

What is a line segment?

A segment has two endpoints and contains every point between them. Segment AB and segment BA name the same segment: reversing the endpoint names does not change it. In geometry notation, a bar over AB names the segment, while AB without the bar often means its length. For example, AB = 5 cm states a measurement.

A line continues forever in both directions. A ray starts at one endpoint and continues forever in one direction. A segment ends at both endpoints, so its entire length can be measured. A line or ray has no finite total length, although a segment drawn on it does.

How to measure a line segment with a ruler

1. Choose the correct scale, such as centimeters or inches. Keep the same unit throughout the measurement.
2. Place the ruler along the segment. Align an endpoint with the zero mark, which may be slightly inside the ruler’s edge.
3. Read the mark at the other endpoint. Count the smaller divisions when the endpoint falls between whole-number marks.
4. Write the length with its unit. An endpoint at 5 cm, with the other at zero, gives CD = 5 cm.

If the segment does not start at zero, subtract the readings. Endpoints at the 2 cm and 7.5 cm marks give a length of 7.5 − 2 = 5.5 cm. Reading only the far endpoint would give the wrong length.

On a number line, use the distance between the endpoint coordinates: larger coordinate minus smaller coordinate. Endpoints at −3 and 4 give a length of 4 − (−3) = 7 units. Length is never negative. Do not measure a printed diagram to find an exact answer unless the instructions say it is drawn to scale.

The segment addition postulate: add parts to find the whole

If G lies between E and F on the same straight segment, then EG + GF = EF. The two smaller lengths add to the whole. If you know the whole and one part, subtract to find the missing part.

Worked examples

Add the parts: G is between E and F, EG = 2 cm, and GF = 3 cm. Therefore EF = 2 + 3 = 5 cm.

Find a missing part: J is between H and I, HI = 8 cm, and HJ = 3 cm. Since HJ + JI = HI, JI = 8 − 3 = 5 cm. Check: 3 + 5 = 8.

The word “between” matters. Knowing two lengths alone does not tell you which is the whole; first identify the endpoint order.

Congruent segments and midpoints

Congruent segments have equal lengths. They may point in different directions or appear in different places. If AB = 6 cm and CD = 6 cm, the two segments are congruent.

A midpoint lies on a segment and divides it into two congruent parts. If M is the midpoint of AB and AB = 12 cm, then AM = MB = 6 cm. A point merely lying between the endpoints is not necessarily the midpoint.

On a number line, average the endpoint coordinates to find the midpoint. For endpoints −3 and 5, the midpoint coordinate is (−3 + 5) ÷ 2 = 1. Each half has length 4 units; the whole has length 8 units. The midpoint’s coordinate and the segment’s length are different quantities.

Practice: try first, then open the worked answers

1. KL = 10 cm, KM = 4 cm, and M is between K and L. Find ML.
2. VW = 18 cm, VX = 7 cm, and X is between V and W. Find XW.
3. EG = 24 cm, GF = 9 cm, and G is between E and F. Find EF.
4. A ruler shows endpoints at 3 cm and 8.5 cm. Find the segment’s length.
5. M is the midpoint of AB, and AM = 7 cm. Find AB.

Further practice

For printable geometry and measurement practice, browse the Grade 4 math worksheet collection. Use the topic headings to choose line segments or distance measurement, then return to the examples above when checking your method.

Reference: Common Core measurement tools standard; OpenStax explanation of distance and midpoints.

Line vs ray vs line segment

A quick way to identify a segment in a drawing: look at both ends. If both ends are dots and there are no arrows, it is a line segment. The sides of a triangle and the edges of a square are all line segments.

Midpoint and length on the coordinate plane

When a segment’s endpoints are points (x₁, y₁) and (x₂, y₂), two formulas do the work.

• Midpoint: M = ((x₁ + x₂)/2, (y₁ + y₂)/2). Average the x-values and average the y-values.
• Length (distance): d = √((x₂ − x₁)² + (y₂ − y₁)²). This comes from the Pythagorean theorem.

Example: A(1, 2) and B(7, 10).

1. Midpoint: ((1 + 7)/2, (2 + 10)/2) = (4, 6).
2. Length: √((7 − 1)² + (10 − 2)²) = √(36 + 64) = √100 = 10.

Check: the distance from A to M is √(3² + 4²) = 5, which is half of 10.

Frequently Asked Questions

What is a line segment in geometry?

A line segment is the straight part of a line between two endpoints, and it includes both endpoints. Unlike a line, it does not go on forever, so it has a length you can measure. On a number line, the segment from 3 to 11 has length 11 − 3 = 8 units. The side of a triangle and the edge of a table are everyday examples.

What is the difference between line segments and rays?

A line segment has two endpoints and a fixed, measurable length. A ray has only one endpoint and continues forever in one direction, so it has no total length. In drawings, a segment has no arrows, while a ray has an arrow on one end. A flashlight beam is often used as a model of a ray, while a pencil models a segment.

How do you name line segments?

Name a line segment by its two endpoints with a bar over the letters, such as segment PQ. The order does not matter, so PQ and QP name the same segment. When you write PQ without the bar, it usually means the length of the segment, as in PQ = 6 cm. Always use the endpoints, not points in the middle.

How many line segments are there in a triangle?

A triangle has 3 line segments, which are its sides. Each side joins two of the three vertices, so triangle ABC has sides AB, BC and CA. If extra points or lines are drawn inside the figure, count again carefully: every pair of points connected by a straight path along the drawing forms another segment.

How many line segments can be formed by joining 3 points?

If no three of the points lie on the same line, 3 points form 3 line segments, one for each pair. In general, n points with no three in a line give n(n − 1) ÷ 2 segments. So 4 points give 4 × 3 ÷ 2 = 6 segments, and 5 points give 5 × 4 ÷ 2 = 10. If all 3 points lie on one line, they still mark 3 segments along it.

How are line segments congruent?

Two line segments are congruent when they have the same length, written AB ≅ CD when AB = CD. Their position or direction does not matter. A midpoint splits a segment into two congruent halves. For the segment from (1, 2) to (7, 10), the midpoint is (4, 6), and each half is 5 units long, since the full length is √(6² + 8²) = 10.