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,
Triangle group plane, the two-dimensional sphere, the real projective plane, or the hyperbolic plane generated by the reflections in the sides of a triangle with angles π/"l", π/"m" and π/"n" (measured in radians). The product of the reflections in two adjacent sides is a rotation by the angle which is twice the angle between those sides, 2π/"l", 2π/"m" and 2π/"n". Therefore, if the generating reflections are labeled "a", "b", "c" and the angles between them in the cyclic order are as given above, then the following relations hold: It is a theorem that all other relations between "a, b, c" are consequences