Triangle Congruence Postulates Page 5 of 5
What about SSA? If two sides and the non-included angle are congruent, are the triangles congruent? No, and it's not just because SSA spells a bad word backwards. SSA just doesn't work to prove that two triangles are congruent.
It's possible to draw two different triangles with these requirements that are not congruent. Take a look at the two triangles below. They have two sets of congruent sides and a non-included angle. See how the side on the right can be rotated out to form a larger triangle? This is why SSA doesn't guarantee that two triangles will be the same. When the angle is included between the two sides (in SAS), it's as if the top angle gets locked into place to prevent this from happening.
Ready to try using SSS, SAS, ASA, and AAS to prove triangles are congruent on your own? Click the START button below to try a practice quiz.