Foundations of geometry and therefore are valid theorems in absolute geometry. Proposition I.31 proves the existence of parallel lines (by construction). Also, the Saccheri–Legendre theorem, which states that the sum of the angles in a triangle is at most 180°, can be proved. The theorems of absolute geometry hold in hyperbolic geometry as well as in Euclidean geometry. Absolute geometry is inconsistent with elliptic geometry: in elliptic geometry there are no parallel lines at all, but in absolute geometry parallel lines do exist. Also, in elliptic geometry, the sum of the angles in any triangle is greater than 180°. Logically, the axioms do
Right triangle right triangle, see the hyperbolic triangle of a hyperbolic sector. The values of the trigonometric functions can be evaluated exactly for certain angles using right triangles with special angles. These include the "30-60-90 triangle" which can be used to evaluate the trigonometric functions for any multiple of π/6, and the "45-45-90 triangle" which can be used to evaluate the trigonometric functions for any multiple of π/4. Let "H", "G", and "A" be the harmonic mean, the geometric mean, and the arithmetic mean of two positive numbers "a" and "b" with "a" > "b". If a right triangle has legs "H"