length. (This is a total of six equalities, but three are often sufficient to prove congruence.) Some individually necessary and sufficient conditions for a pair of triangles to be congruent are: SAS Postulate: Two sides in a triangle have the same length as two sides in the other triangle, and the included angles have the same measure. ASA: Two interior angles and the included side in a triangle have the same measure and length, respectively, as those in the other triangle. (The included side for a pair of angles is the side that is common to them.) SSS: Each side of a triangle has the same length as a corresponding side of the other triangle. AAS: Two angles and a corresponding (non-included) side in a triangle have the same measure and length, respectively, as those in the other triangle. (This is sometimes referred to as AAcorrS and then includes ASA above.) Some individually sufficient conditions are: Hypotenuse-Leg (HL) Theorem: The hypotenuse and a leg in a right triangle have the same length as those in another right triangle. This is also called RHS (right-angle, hypotenuse, side). Hypotenuse-Angle Theorem: The hypotenuse and an acute angle in one right triangle have the same length and measure, respectively, as those in the other right triangle. This is just a particular case of the AAS theorem. An important condition is: Side-Side-Angle (or Angle-Side-Side) condition: If two sides and a corresponding non-included angle of a triangle have the same length and measure, respectively, as those in another triangle, then this is not sufficient to prove congruence; but if the angle given is opposite to the longer side of the two sides, then the triangles are congruent. The Hypotenuse-Leg Theorem is a particular case of this criterion. The Side-Side-Angle condition does not by itself guarantee that the triangles are congruent because one triangle could be obtuse-angled and the other acute-angled. Using right triangles and the concept of similarity, the trigonometric functions sine and cosine can be defined. These are functions of an angle which are investigated in trigonometry. Right triangles A central theorem is the Pythagorean theorem, which states in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two other sides. If the hypotenuse has length c, and the legs have lengths a and b, then the theorem states that The converse