Actually, there is an angle, side side congruence relationship. I do not think it is a postulate, I think it is a theorem. It is angle, small side, large side. If the included angle is smaller than the opposite angle, or congruent to it, then the triangles must be congruent because the opposite side cannot "swing" under the angle to form two triangles. Hypotenuse leg is a special case of the theorem. I always teach this to my students and then ask them why they think it is not included in the text. I have found it useful in at least one quite difficult problem I was trying to solve.
John Benson Evanston Township High School 715 South Boulevard 1600 Dodge Avenue Evanston Il 60202-2907 Evanston IL 60204 847) 328-8019 (phone & fax) (847) 424-7600 (847) 226-7713 ( cell)