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 equilateral dimension is the maximum number of disjoint translates that can all touch each other. For a normed vector space of dimension "d", the equilateral dimension is at most 2; that is, the L norm has the highest equilateral dimension among all normed spaces. asked whether every normed vector space of dimension "d" has equilateral dimension at least , but this remains unknown. There exist normed spaces in any dimension for which certain sets of four equilateral points cannot be extended to any larger equilateral set but these spaces may have larger equilateral sets that do not include these four