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,
Isosceles triangle triangles with sides unequal to the base, and becomes an equality for the equilateral triangle. The area, perimeter, and base can also be related to each other by the equation If the base and perimeter are fixed, then this formula determines the area of the resulting isosceles triangle, which is the maximum possible among all triangles with the same base and perimeter. On the other hand, if the area and perimeter are fixed, this formula can be used to recover the base length, but not uniquely: there are in general two distinct isosceles triangles with given area formula_5 and perimeter