Space (mathematics) projective geometry nor defined from the notions mentioned there. The question "what is the sum of the three angles of a triangle" is meaningful in Euclidean geometry but meaningless in projective geometry. A different situation appeared in the 19th century: in some geometries the sum of the three angles of a triangle is well-defined but different from the classical value (180 degrees). Non-Euclidean hyperbolic geometry, introduced by Nikolai Lobachevsky in 1829 and János Bolyai in 1832 (and Carl Friedrich Gauss in 1816, unpublished) stated that the sum depends on the triangle and is always less than 180 degrees. Eugenio Beltrami
Triangle the hypotenuse equals the sum of the squares of the lengths of the two other sides. If the hypotenuse has length "c", and the legs have lengths "a" and "b", then the theorem states that The converse is true: if the lengths of the sides of a triangle satisfy the above equation, then the triangle has a right angle opposite side "c". Some other facts about right triangles: For all triangles, angles and sides are related by the law of cosines and law of sines (also called the "cosine rule" and "sine rule"). The triangle inequality states that the sum