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,
Angle bisector theorem of the length of side "AB" to the length of side "AC": and conversely, if a point "D" on the side "BC" of triangle "ABC" divides "BC" in the same ratio as the sides "AB" and "AC", then "AD" is the angle bisector of angle "∠ A". The generalized angle bisector theorem states that if "D" lies on the line "BC", then Angles "∠ BAD" and "∠ DAC" are equal. Therefore, the right hand sides of equations () and () are equal, so their left hand sides must also be equal. which is the angle bisector theorem. If angles "∠