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Euclidean geometry
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Three theorems of congruent triangles Proof that the sum of the angles in a triangle is 180 degrees Fundamental theorem of similarity Area of a triangle Pythagorean theorem Chord in a circle Three-dimensional shapes Platonic solids Figure 2: Illustration of Euclid's fifth postulate (see text). A blue quadrilateral labeled ABCD with diagonals intersecting inside, forming four triangles; right angles are marked at corners A and B, and tick marks indicate equal side lengths. Text explains triangle congruence and angle equality within the quadrilateral.
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Euclidean geometry summary
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Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.
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Three theorems of congruent triangles
Three theorems of congruent triangles This diagram depicts three basic theorems that triangles are congruent—that is, they are of equal shape and size—if: (1) two sides and the included angle are equal, designated SAS; (2) two angles and the included side are equal, designated ASA; or (3) all three sides are equal, designated SSS.

Euclidean geometry

mathematics
Written by
Benno Artmann
Professor Emeritus of Mathematics at the University of Goettingen, Goettingen, Germany. Author of Euclid: The Creation of Mathematics.
Benno Artmann
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Britannica Editors
Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree....
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Euclidean geometry, the study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid (c. 300 bce). In its rough outline, Euclidean geometry is the plane and solid geometry commonly taught in secondary schools. Indeed, until the second half of the 19th century, when non-Euclidean geometries attracted the attention of mathematicians, geometry meant Euclidean geometry. It is the most typical expression of general mathematical thinking. Rather than...

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