Euclidean geometry equal (SAS), or two angles and a side equal (ASA) (Book I, propositions 4, 8, and 26). Triangles with three equal angles (AAA) are similar, but not necessarily congruent. Also, triangles with two equal sides and an adjacent angle are not necessarily equal or congruent. The sum of the angles of a triangle is equal to a straight angle (180 degrees). This causes an equilateral triangle to have three interior angles of 60 degrees. Also, it causes every triangle to have at least two acute angles and up to one obtuse or right angle. The celebrated Pythagorean theorem (book I,
Equilateral dimension manifold but arbitrarily high equilateral dimension. Equilateral dimension In mathematics, the equilateral dimension of a metric space is the maximum number of points that are all at equal distances from each other. Equilateral dimension has also been called "metric dimension", but the term "metric dimension" also has many other inequivalent usages. The equilateral dimension of a "d"-dimensional Euclidean space is , and the equilateral dimension of a "d"-dimensional vector space with the Chebyshev distance (L norm) is 2. However, the equilateral dimension of a space with the Manhattan distance (L norm) is not known; Kusner's conjecture, named after Robert B.