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 (in fact, this formula holds for "all" tangential polygons), and where formula_59 are the radii of the excircles tangent to sides "a, b, c" respectively. We also have and for circumdiameter "D"; and for angle α ≠ 90°. The area can also be expressed as In 1885, Baker gave a collection of over a hundred distinct area formulas for the triangle. These include: for circumradius (radius of the circumcircle) "R", and The area "T" of any triangle with perimeter "p" satisfies with equality holding if and only if the triangle is equilateral. Other upper bounds on the area "T" are