Lines, Rays & Segments | Geometry Learning

📏Straight Lines

Definition:

A straight line has no endpoints and extends infinitely in both directions.

Key Properties:

•Infinite length: Lines extend forever in both directions
•Two-point rule: Any two distinct points determine exactly one line
•No thickness: Lines are one-dimensional

Representation:

Lines are typically represented by lowercase letters (a, b, c) or by naming two points on the line with a double-headed arrow (↔) above them.

Key Concept: Through any two points, there is exactly one straight line. This is one of the fundamental postulates of geometry.

➡️Rays

Definition:

A ray has one endpoint and extends infinitely in one direction.

Key Properties:

•One endpoint: Called the origin or starting point of the ray
•Infinite in one direction: Extends forever from the endpoint
•Part of a line: A ray is a portion of a straight line

Representation:

Rays are named using the endpoint first, followed by any other point on the ray, with a single-headed arrow (→) above them. For example: ray OA starts at point O and passes through point A.

Important: The order matters when naming rays. Ray OA is different from ray AO if they start from different points.

—Line Segments

Definition:

A line segment has two endpoints and cannot extend in either direction. It has a measurable length.

Key Properties:

•Two endpoints: Both ends are clearly defined points
•Finite length: Can be measured using a ruler
•Shortest distance: The shortest path between two points

Representation:

Line segments are named using their endpoints, often written as AB or with a line above the letters. The length of segment AB is written as |AB| or AB.

Fundamental Principle: Between any two points, the line segment is the shortest possible path. This is known as the "shortest distance principle."

Quick Comparison

Type	Endpoints	Length	Symbol
Line	None (0)	Infinite	↔AB or line l
Ray	One (1)	Infinite	→AB
Segment	Two (2)	Finite/Measurable	AB or AB̄

Practice Tips

Visual Recognition:

• Lines have arrows on both ends
• Rays have an arrow on one end
• Segments have dots/points on both ends

Common Applications:

• Lines: Roads, horizons
• Rays: Light beams, laser pointers
• Segments: Rulers, edges of objects