Why isn't ASS a member of the "Fab Five"?
I have taught Geometry for many years, and a big part of the curriculum has been proving congruent triangles. If you teach this, you know about what I refer to as the "Fab Five": Angle-Side-Angle (ASA) Side-Angle-Side (SAS) Side-Side-Side (SSS) Angle-Angle-Side (AAS) Hypotenuse-Leg of a Right Triangle (HL Rt. △) I introduce this list with accompanying diagrams illustrating each method. Here is a sample: After generating the list of the "Fab Five", I emphasize to the students that each method requires three parts from each triangle. This, in turn, always results with students asking: "Hey Mr. K. What about AAA and ASS?", the latter of which usually produces a number of giggles. So I ask them: "If you know that three angles in one triangle are congruent to the three corresponding angles in another triangle, why are the triangles not necessarily congruent?" After a little guidance, students will recall our work from earlier in