A segment is the simplest geometric object: a straight connection between two points. A line is the same connection extended infinitely in both directions.

• A segment has two endpoints.
• A line has no endpoints.
• A segment is used to define distance.
• A line is used to define direction.

Why Lines Matter in Geometry

Lines establish direction, alignment, and structure. They are the backbone of perpendiculars, parallels, grids, and page frameworks. A single line can define the orientation of an entire construction.

Segments as Measured Relationships

A segment is not a number. It is a relationship between two points. In ruler‑and‑compass geometry, segments are compared, copied, and transferred—not measured. This keeps the work grounded in proportion rather than arithmetic.

Lines and Segments in Constructions

Most constructions begin by marking two points and joining them with a segment. That segment becomes the base for perpendiculars, bisectors, squares, and many other forms. Extending the segment into a line gives you a direction that can be used repeatedly throughout the drawing.

Step‑by‑Step: Drawing a Segment

• Mark two points on the page.
• Place the straightedge so it passes through both points.
• Draw a clean stroke between them.
• Keep the pressure light and the movement steady.
• Label the points if needed for later steps.

Step‑by‑Step: Extending a Segment into a Line

• Place the straightedge along the segment.
• Extend the stroke beyond both endpoints.
• Keep the extension straight and continuous.
• A line has no fixed length; extend it as far as needed for the construction.

Notes for Practice

• A clean segment is the foundation of many constructions.
• Avoid measuring unless absolutely necessary.
• Use consistent notation for points and lines.
• A line can be extended at any time; a segment can be copied with a compass.