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 center if the trilinear coordinates of P can be expressed in the form f(A) : f(B) : f(C) where f(A) is a function of the angle A alone and does not depend on the other angles or on the side lengths. A triangle center P is called a "transcendental triangle center" if P has no trilinear representation using only algebraic functions of a, b and c. Let "f" be a triangle center function. If two sides of a triangle are equal (say "a" = "b") then so two components of the associated triangle center are always equal. Therefore all triangle centers