Euclidean geometry: Quick Facts

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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

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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Topics

Thales’ rectangle fundamental theorem of similarity Cavalieri’s principle method of indivisibles Pythagorean theorem side-angle-side theorem triangle inequality method of exhaustion quadrature parallel postulate topology analytic geometry differential geometry projective geometry non-Euclidean geometry algebraic geometry catastrophe theory Pappus’s theorem Ceva’s theorem length, area, and volume

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geometry: Euclidean geometry

Key People

Euclid

Euclid

Greek mathematician

David Hilbert

David Hilbert

German mathematician

Maryam Mirzakhani

Maryam Mirzakhani

Iranian mathematician

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Adrien-Marie Legendre

French mathematician

Equations written on blackboard

All About Math Quiz

Equations written on blackboard

Numbers and Mathematics

Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.

Define It: Math Terms