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 near-cancellation between the semiperimeter and side length in those triangles. If the apex angle formula_7 and leg lengths formula_8 of an isosceles triangle are known, then the area of that triangle is: This is a special case of the general formula for the area of a triangle as half the product of two sides times the sine of the included angle. The perimeter formula_10 of an isosceles triangle with equal sides formula_2 and base formula_3 is just As in any triangle, the area formula_5 and perimeter formula_10 are related by the isoperimetric inequality This is a strict inequality for isosceles