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,
Bisection The interior angle bisectors of a triangle are concurrent in a point called the incenter of the triangle, as seen in the diagram at right. The bisectors of two exterior angles and the bisector of the other interior angle are concurrent. Three intersection points, each of an external angle bisector with the opposite extended side, are collinear (fall on the same line as each other). Three intersection points, two of them between an interior angle bisector and the opposite side, and the third between the other exterior angle bisector and the opposite side extended, are collinear. The angle bisector theorem