[Kortni]

Ok, can anyone tell me the difference in the ASA postulate and the AAS postulate??? I am really cunfused because they are both two angles and a side!!!! ACH!!!!!!!!!!!!!!!!! I love geometry, I'm just slightly confused.....why arent the two postulates interchangable?


Thanks so much for your help!
-Kortni

Both of these postulates can be used to prove that two triangles are congruent (same sides and same angles in the same order).

The difference, concisely put, is that the order the angles and sides must be checked is different between the AAS and and ASA postulates. This may already have been obvious since the order is also the only difference in their acronyms. Consider the following two triangles:
(I hope these come out alright.)



(Note: the sides are intentionally labeled the lowercase of the angle they are across from. I will use these labels for now on.)

Although it's obvious these triangles are drawn to appear congruent, that's not a rigorous mathematical proof. To use the ASA postulate, you must find and Angle-Side-Angle group which is the same on both triangles. For instance, if you know that B-c-A is the same as E-f-D (B=E,c=f,D=A), then the ASA postulate says that the triangles are congruent. In order to use this postulate, you MUST find angle right beside a side right beside another angle. These can't be separated by other sides or angles.

The AAS postulate is similar, but now you're looking for the line in a different place. Instead of being between the two angles, it should be right next to one and opposite the other. For instance, if you know that B-A-b is the same as E-D-e (B=E,A=D,b=e), then the AAS postulate says that the triangles are congruent.

You observed correctly that they both have two angles. The difference is where the side must be with respect to those angles. As it turns out, since both AAS and ASA are sufficient for proving the triangles' congruence, if you find any order of two angles and a side being the same between two triangles, you know they must be congruent.

Hope I was helpful. If you still have questions, feel free to email me and I'd be glad to try to help more!
packman@carolina.rr.com

~Shaun

[Kortni]

Shuan,
Thank you sooooooooooooooooooooooooo much for your help!! That makes, like, total sense!! Thanks again, bro.
I will be keeping your email address incase I run into more difficulties!

-kortni

[Phil]

Originally posted by Kortni
Shuan,
Thank you sooooooooooooooooooooooooo much for your help!! That makes, like, total sense!! Thanks again, bro.
I will be keeping your email address incase I run into more difficulties!

-kortni

Well I'm glad you get it.

Its pretty simple though...

Basically, if there is the congruent side is between the two congruent angles, then it is ASA, because that is the order it goes in.

If not, then it is AAS