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 β is the interior angle at "B", formula_28 is the interior angle at "C" and "c" is the line AB). Furthermore, since sin α = sin ("π" − α) = sin (β + formula_28), and similarly for the other two angles: "Knowing AAS": and analogously if the known side is "a" or "c". "Knowing ASA": and analogously if the known side is "b" or "c". The shape of the triangle is determined by the lengths of the sides. Therefore, the area can also be derived from the lengths of the sides. By Heron's formula: where formula_34 is the semiperimeter, or