Proofs with Triangles

Question

I have been studying how to prove that triangles are congruent. I have been able to identify the rules concerning side and angle congruency, but am having a hard time determining if two triangles fall into ASA or AAS.

How do you read a problem such as this and determine the order, if you know that there are two congruent angles and one congruent side?

Thanks for any clarification,

Brian

Answer 1

ASA means two angles and an included side are equal. If you have triangles ABC and DEF congruent, then ASA would apply if angles A and B are equal to angles D and E, respectively, and the included sides, AB and DE are equal.

AAS means two angles and a non-included side are equal. AAS would apply to our example if once again angles A and B are equal to angles D and E, respectively, and non-included sides, BC and EF are equal.

B E

/ \ / \

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/ \ / \

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/ \ / \

A /------------\ C D /--------------\ F