Why Doesn't SSA Work

Harry Drew
Two triangles have side lengths of 6 and 8 units.  And the next angle following the 8 unit side is .  If the SSA method always proved congruence, then these two triangles would match.  However, consider the illustration above.  Swing the 6 unit side like a pendulum through the two points of intersection.  Notice that two triangles can be formed that are not congruent.