Geometry

Points, Lines & Rays

Drawing and identifying points, lines, line segments, rays, and angles.

Intermediate15 min lesson3 min readUpdated August 12, 2026Author not yet attributed

The Building Blocks of Shapes

Every shape studied so far is built from a small set of basic geometric objects. Naming these building blocks precisely — points, lines, line segments, and rays — makes it possible to describe and classify shapes with real mathematical precision.

Definition — Point, Line, Line Segment, and Ray

A point is an exact location with no size. A line extends infinitely in both directions. A line segment is a straight path between two endpoints. A ray starts at one endpoint and extends infinitely in only one direction.

Two lines that never cross, no matter how far they extend, are called parallel. Two lines that cross at a right angle (90 degrees) are called perpendicular. Both relationships come up constantly when describing and classifying two-dimensional shapes.

Worked Example — Identifying Geometric Objects

A diagram shows a straight path with two labeled endpoints, A and B. What is this object called? Since it has two distinct endpoints and doesn't extend infinitely, it's a line segment, written as segment AB.

Worked Example — Identifying Parallel and Perpendicular Lines

Two lines on a grid never touch no matter how far they're extended, while a third line crosses one of them forming a perfect right angle. Describe the relationships. The two lines that never touch are parallel. The line that crosses the other one at a right angle is perpendicular to it.

Geometry Canvas

Point mode (click to add a point)LabelsMeasurementsSnap to grid

Construct

Tool

Objects

1.
Color
P1
P1: a free point, draggable on the plane
2.
Color
P2
P2: a free point, draggable on the plane
3.
Color
P3
P3: a free point, draggable on the plane
4.
Color
poly1
poly1: the polygon through P1, P2, P3

Measurements

poly1area = 15perimeter = 17.66

Tip

A ray is named by its endpoint first, then any other point along it — ray AB starts at A and passes through B, which is different from ray BA, which would start at B instead.

Common Mistakes

Confusing a line segment (with two endpoints) with a ray (with only one endpoint, extending infinitely in the other direction).
Check how many endpoints the object has — two endpoints means a line segment; exactly one endpoint, with the object continuing forever in the other direction, means a ray.
Assuming any two lines that look close to a right angle in a drawing are automatically perpendicular.
Perpendicular lines must cross at exactly 90 degrees — check the angle with a protractor or right-angle marker rather than judging by appearance alone.

Key Takeaways

A line segment has two endpoints; a ray has one endpoint and extends infinitely in one direction; a line extends infinitely in both directions.
Parallel lines never cross; perpendicular lines cross at exactly a right angle.
Precisely naming these basic objects makes describing and classifying shapes possible.

Summary

Points, lines, rays, and their relationships are the vocabulary every shape is described with. The final lesson uses that vocabulary to classify two-dimensional shapes by their lines and angles.

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