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,
Inscribed angle "V" and whose sides pass through points "A" and "B". Draw line "OA". Angle "BOA" is a central angle; call it "θ". Lines "OV" and "OA" are both radii of the circle, so they have equal lengths. Therefore, triangle "VOA" is isosceles, so angle "BVA" (the inscribed angle) and angle "VAO" are equal; let each of them be denoted as "ψ". Angles "BOA" and "AOV" are supplementary. They add up to 180°, since line "VB" passing through "O" is a straight line. Therefore, angle "AOV" measures 180° − "θ". It is known that the three angles of a triangle add