Geometry Terms: Definitions, Symbols, and Diagram Language

Geometry terms are the shared vocabulary of the subject. Point, line, and plane are the three undefined terms every other figure is built from, and segments, rays, and angles are defined in terms of them. The mark above two letters tells you whether you are looking at a line, a segment, or a ray. Master this notation and the diagram language around it, and theorems, proofs, and constructions become readable at a glance.

Why Geometry Terms Matter

Geometry runs on precise words, and a diagram means only what its notation says. A dropped bar, a reversed ray arrow, or ≅ mistaken for ∼ rewrites the whole problem. This page is a terms-and-notation reference: the undefined building blocks, the symbols above them, and the way diagrams are read. The broader concept map lives in the geometry concepts guide; this page does not restate it.

Undefined Terms: Point, Line, and Plane

Three terms are left undefined because everything else is defined from them. They are not unknown; they are the starting points. The coordinate background for these objects is developed in the plane geometry guide.

• Point — a location with no size. Name it with a capital letter, like P.
• Line — straight and infinite in both directions. Two points on it, or one lowercase letter like ℓ, name it.
• Plane — a flat, two-dimensional surface that extends forever. Name it with a script letter like ℙ or with three points on it.

Stanford's DREME TE glossary defines these basic figures in plain language, the style the definitions below follow; that page was unreachable from the review network, so it stays as institutional background rather than a live link.

Defined Terms Built on Them

Defined terms combine the undefined ones. Three you meet on day one:

Line Segments

A segment is the part of a line between two endpoints, written AB with a bar over the two letters. It has a finite length, written AB with no bar, read "the length of AB". Because both ends are fixed, a segment can be measured with a ruler, and its length is always a positive number.

Rays

A ray has one endpoint and extends forever in one direction. Write it with a one-way arrow, →AB, and keep the endpoint first: →AB starts at A and runs through B. A ray is not an undefined term; a line plus one endpoint builds it.

Angles

An angle is two rays with a common endpoint, the vertex. Name it ∠AOB, where the middle letter O is the vertex; ∠ is read "angle". Sizes get names too: acute, right, and obtuse angles describe how wide the opening is. Defined shapes like polygons build on these terms, and the geometric shapes guide develops the shapes themselves.

Symbols and Notation

The mark above the letters carries the exact meaning. This chart is the core notation; keep it beside the other symbol tables in the geometry formulas and symbols reference.

Line, Segment, Ray

• ↔AB — "line AB", infinite both ways.
• AB̄ — "segment AB", finite, endpoints at both letters.
• →AB — "ray AB", endpoint at A, one-way.
• AB — "the length of AB", a number, no bar.

Read the mark first and then the letters: the double arrow means infinite both ways, the bar means finite, the single arrow means one-way, and the bare pair means a measured number.

Parallel, Perpendicular, Congruent, Similar

• AB ∥ CD — "AB is parallel to CD"; the lines never meet.
• AB ⊥ CD — "AB is perpendicular to CD"; they meet at a right angle.
• △ABC ≅ △DEF — "triangle ABC is congruent to triangle DEF"; matching sides and angles are equal, same shape and same size.
• △ABC ∼ △DEF — "triangle ABC is similar to triangle DEF"; same shape, proportional sides, size may differ. Similarity scaling is worked out step by step in the dilation geometry guide.
• A′ — "A prime", the image of point A after a transformation.

The shared word list behind these entries is cross-checked against the Vocabulary.com geometry list.

How to Read a Geometry Diagram

Diagrams carry meaning through position and marks, not decoration.

Collinear and Coplanar Points

Points are collinear when they sit on one line, and coplanar when they sit in one plane. Three points on the same line are collinear; add a point off the line and the four remain coplanar if they lie in the same plane.

Intersections

Two distinct non-parallel lines meet at exactly one point; parallel lines never meet. A line and a plane meet at one point unless the line lies inside the plane, and two planes meet in a line. Matching tick marks on sides mark those sides as equal in length, and matching arc marks mark those angles as equal.

Common Confusions to Avoid

• ≅ vs ∼: congruent means same shape and same size; similar means same shape only. Swapping them is the most common symbol slip.
• Ray order: →AB starts at A; →BA starts at B. The endpoint comes first.
• "Undefined" does not mean vague: point, line, and plane are deliberate starting points, not words we have not bothered to define.
• Bar or no bar: AB̄ is the segment, the object; AB is its length, a number.

Practice Reading Diagrams

Pick a diagram and read it out loud before solving: name each point, then each line, segment, and ray, then say which pairs are parallel, perpendicular, congruent, or similar. Mark equal sides and angles with their tick marks, and check whether the points you need are collinear or coplanar.

The Gauth Geometry course opens with the same basic terms and notation, which matches this reference. To drill at your own level, open Gauth Math Courses and enter geometry symbols and definitions.

Sources and Review

• Vocabulary.com — Geometry Terms Vocabulary List, reviewed 2026-10-28. Vocabulary reference for term pronunciation and word family.