Thales's theorem theorem is named after Thales because he was said by ancient sources to have been the first to prove the theorem, using his own results that the base angles of an isosceles triangle are equal, and that the sum of angles in a triangle is equal to 180°. Dante's "Paradiso" (canto 13, lines 101–102) refers to Thales's theorem in the course of a speech. The following facts are used: the sum of the angles in a triangle is equal to 180° and the base angles of an isosceles triangle are equal. Since = = , ∆OBA and ∆OBC are isosceles
Solution of triangles third angle by using the angle sum property of a triangle, then find the other two sides using the law of sines. The general spherical triangle is fully determined by three of its six characteristics (3 sides and 3 angles). Note that the sides of a spherical triangle are measured by angular rather than linear units, based on the corresponding central angles. The solution of triangles for non-Euclidean spherical geometry has some differences from the planar case. For example, the sum of the three angles depends on the triangle. In addition, there are no unequal similar triangles, and so the