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,
Reuleaux triangle This is the sharpest possible angle at any vertex of any curve of constant width. Additionally, among the curves of constant width, the Reuleaux triangle is the one with both the largest and the smallest inscribed equilateral triangles. The largest equilateral triangle inscribed in a Reuleaux triangle is the one connecting its three corners, and the smallest one is the one connecting the three midpoints of its sides. The subset of the Reuleaux triangle consisting of points belonging to three or more diameters is the interior of the larger of these two triangles; it has a larger area than the