Geometry begins with simple objects that help us describe space precisely. Lines, line segments, and rays look similar, but they behave differently because of endpoints and direction. These ideas are used in diagrams, proofs, measurement, construction, and coordinate geometry.
Knowing how to name and interpret them makes more advanced geometry much easier.
Key Facts
- A line extends forever in both directions and is named with two points, such as line AB, or with a lowercase letter.
- A line segment has two endpoints and a measurable length, such as segment AB.
- A ray has one endpoint and extends forever in one direction, such as ray AB, where A is the endpoint.
- Segment addition postulate: If B is between A and C, then AB + BC = AC.
- Congruent segments have equal lengths, so if segment AB is congruent to segment CD, then AB = CD.
- On a number line, the length of segment AB is AB = |x2 - x1|.
Vocabulary
- Line
- A straight path of points that extends forever in both directions.
- Line segment
- A part of a line that has two endpoints and a fixed length.
- Ray
- A part of a line that starts at one endpoint and extends forever in one direction.
- Endpoint
- A point at the beginning or end of a segment or the starting point of a ray.
- Congruent segments
- Line segments that have exactly the same length.
Common Mistakes to Avoid
- Naming a ray backward: Ray AB starts at A and passes through B, so ray BA usually represents a different ray with endpoint B.
- Treating a line like it has endpoints: A line extends forever in both directions, so it cannot have a fixed length.
- Using AB + AC = BC when B is between A and C: The correct segment addition relationship is AB + BC = AC.
- Assuming tick marks mean a segment length is known: Tick marks show congruence, not a specific measurement unless a length is labeled.
Practice Questions
- 1 Points A, B, and C are collinear, with B between A and C. If AB = 7 cm and BC = 11 cm, find AC.
- 2 On a number line, point P is at -4 and point Q is at 9. Find the length of segment PQ.
- 3 A diagram shows a straight figure with an arrowhead on the right end only and a solid dot on the left end labeled M, with another point N on the figure to the right. Explain whether it should be named as a line, segment, or ray, and give a correct name for it.