Triangle Congruence: AAS and ASADate: 10/16/2003 at 13:29:34 From: Mrs. Bergeron Subject: Triangle Congruency My 8th grade geometry students (all 2 of them) were wondering why AAS (Angle, Angle, Side) is not a considered a valid method to prove two triangles are congruent. We can't find a way to create two different triangles if they have 2 angles and the non-including side congruent. Can you help us? Date: 10/16/2003 at 15:33:28 From: Doctor Peterson Subject: Re: Triangle Congruency Hi, Mrs. Bergeron. The fact is, AAS is a perfectly good way to prove congruence of triangles. It's easy to prove: if two angles of a triangle are congruent to corresponding angles in another, then the third angles are also congruent, since the sum of the angles in each has to be 180 degrees. So you really have all three angles congruent, and can apply the ASA theorem, using the two angles adjacent to the side S, in order to prove congruence. So AAS is just a quick corollary of ASA, which is probably why it is not mentioned much. Commonly when you need to use it you can just use the argument above within your proof to show that all three angles are congruent, and then use ASA; so you don't need to have AAS in your arsenal. But it is certainly useful to be aware of it. Of course, SSA is not valid; you have probably seen some of our explanations of that fact. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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