Same as the Angle Side Side Postulate (ASS)

What about SSA (Side Side Angle) theorem?

There is NO SUCH THING!!!! The ASS Postulate does not exist because an angle and two sides does not guarantee that two triangles are congruent.

If two triangles have two congruent sides and a congruent non included angle, then triangles are NOT NECESSARILLY congruent. This is why there is no Side Side Angle (SSA) and there is no Angle Side Side (ASS) postulate. The way that many people remember this fact is that the ASS postulate would be the name for a donkey! (ASS) And there is no postulate named after a donkey!

However, if you would like a picture to illustrate why there is no ASS or SSA postulate look at the two triangles below.

As you can see, even though side BC = BD , this side length is able to swivel such that two non congruent triangles are created even though they have two congruent sides and a congruent, non included angle. (SSA)

ABC ABD

The two triangles are NOT congruent WHY NOT SSA