AA postulate congruent angles. AA postulate In Euclidean geometry, the AA postulate states that two triangles are similar if they have two corresponding angles congruent. The AA postulate follows from the fact that the sum of the interior angles of a triangle is always equal to 180°. By knowing two angles, such as 32° and 64° degrees, we know that the next angle is 84°, because 180-(32+64)=84. (This is sometimes referred to as the AAA Postulate—which is true in all respects, but two angles are entirely sufficient.) The postulate can be better understood by working in reverse order. The two triangles on
Integer triangle harmonic progression. This is because such angles have to be rational angles of the form with rational 0 < < 1. But all the angles of integer triangles must have rational cosines and this will occur only when = i.e. the integer triangle is equilateral. The square of each internal angle bisector of an integer triangle is rational, because the general triangle formula for the internal angle bisector of angle "A" is formula_2 where "s" is the semiperimeter (and likewise for the other angles' bisectors). Any altitude dropped from a vertex onto an opposite side or its extension will split