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,
Hyperbolic triangle scale is most convenient if the lengths are measured in terms of the absolute length (a special unit of length analogous to a relations between distances in spherical geometry). This choice for this length scale makes formulas simpler. In terms of the Poincaré half-plane model absolute length corresponds to the infinitesimal metric formula_1 and in the Poincaré disk model to formula_2. In terms of the (constant and negative) Gaussian curvature of a hyperbolic plane, a unit of absolute length corresponds to a length of In a hyperbolic triangle the sum of the angles "A", "B", "C" (respectively opposite to the