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,
Schwarz triangle function Δ has angles /"a", /"b" and /"c" with "a", "b", "c" integers greater than 1. The hyperbolic area of Δ equals – /"a" – /"b" – /"c", so that The construction of a tessellation will first be carried out for the case when "a", "b" and "c" are greater than 2. The original triangle Δ gives a convex polygon "P" with 3 vertices. At each of the three vertices the triangle can be successively reflected through edges emanating from the vertices to produce 2"m" copies of the triangle where the angle at the vertex is /"m". The triangles do not