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
Incircle and excircles of a triangle any vertex to the incircle tangency on either adjacent side is half the sum of the vertex's adjacent sides minus half the opposite side. Thus for example for vertex "B" and adjacent tangencies "T" and "T", The incircle radius is no greater than one-ninth the sum of the altitudes. The squared distance from the incenter "I" to the circumcenter "O" is given by and the distance from the incenter to the center "N" of the nine point circle is The incenter lies in the medial triangle (whose vertices are the midpoints of the sides). The radius of the incircle is