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,
Equilateral triangle the location of "P". Pompeiu's theorem states that, if "P" is an arbitrary point in an equilateral triangle "ABC", then there exists a triangle with sides of lengths "PA", "PB", and "PC". That is, "PA", "PB", and "PC" satisfy the triangle inequality that any two of them sum to at least as great as the third. By Euler's inequality, the equilateral triangle has the smallest ratio "R"/"r" of the circumradius to the inradius of any triangle: specifically, "R"/"r" = 2. The triangle of largest area of all those inscribed in a given circle is equilateral; and the triangle of smallest