what does this symbol mean?

Geometry symbols

The symbols of school geometry, from ∠ and △ to ≅ and ∼, ⊥ and ∥, the arc, and the marks over AB for a line, ray and segment, what each one means.

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Shapes and angles 4 symbols

Relations 4 symbols

About geometry symbols

Geometry symbols are the shorthand of school geometry: ∠ for an angle and △ for a triangle; ≅ and ∼ for figures that match exactly or in shape only; ⊥ and ∥ for lines that meet at a right angle or never meet; and marks drawn over a pair of letters for an arc or a line, ray or segment. Each page says what one symbol means and how it is read in a statement such as △ABC ≅ △DEF, “triangle ABC is congruent to triangle DEF”. The readings are from OpenStax’s Contemporary Mathematics and Henry Africk’s Elementary College Geometry (CUNY New York City College of Technology); the histories are from Jeff Miller’s Earliest Uses of Various Mathematical Symbols and Florian Cajori’s A History of Mathematical Notations (1928). Angles are measured with the degree sign °, which has its page in Punctuation and typographic symbols, and π is in Greek letters.

Pictures, signs and algebra

Cajori sorted the symbols of geometry roughly under three heads: pictographs, small pictures of the thing meant, such as the triangle; ideographs designed especially for geometry, such as ∼ for “similar”; and the symbols of elementary algebra. Some pictographs are ancient: Miller records Heron using a triangle for a triangle around AD 150. Cajori found them exceptional, unknown to other writers for about a thousand years afterwards. Pierre Hérigone’s Cursus mathematicus of 1634 showed what Cajori called an eruption of symbols, among them signs for angle and perpendicular.

School geometry and engineering drawings

Four of these shapes also appear on technical drawings, with a different meaning. In a feature control frame, ∠, ⟂, ∥ and ⌒ are tolerances on a manufactured part: angularity, perpendicularity, parallelism and profile of a line. The UK National Physical Laboratory’s guide to drawings defines each by a tolerance zone, such as two planes perpendicular to a datum that a surface must lie between. In geometry, AB ⊥ CD is an exact statement about two lines; on a drawing, the symbol sets how far a real surface may stray from that. The drawing symbols are in GD&T symbols.

Sources

  1. Elementary College Geometry, 2.1 The Congruence Statement, Henry Africk, Elementary College Geometry (CUNY New York City College of Technology, 2021), CUNY Academic Works, via LibreTexts, The congruence statement
  2. Contemporary Mathematics, 10.1 Points, Lines, and Planes, OpenStax (Rice University), Basic geometric symbols; parallel and perpendicular lines
  3. A History of Mathematical Notations, Vol. I: Notations in Elementary Mathematics, Florian Cajori (Chicago: Open Court, 1928); full text of the Wellcome Collection copy, Internet Archive, §§ 357, 359
  4. Earliest Uses of Symbols from Geometry, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Triangle; Angle; Perpendicularity
  5. Fundamental Good Practice in the Design and Interpretation of Engineering Drawings for Measurement Processes, Measurement Good Practice Guide No. 79, David Flack and Keith Bevan, 2005, National Physical Laboratory (UK), Chapter 4, Tolerances of orientation; Profile

Researched, edited and approved by Rory Hansen before publishing. Last reviewed October 9, 2026. How we research