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,
Schwarz triangle function a vertex of the polygon "P" makes an angle of less than 2/3 with each of the edges of the polygon at that vertex if exactly two triangles of "P" meet at the vertex, since each has an angle less than or equal to /3 at that vertex. To check this is true when three triangles of "P" meet at the vertex, "C" say, suppose that the middle triangle has its base on a side "AB" of "P". By induction the radii "OA" and "OB" makes angles of less than or equal to 2/3 with the edge "AB". In this