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Thread: ASA

  1. #1
    Sep 2010


    I have a question:

    Are two triangles congruent if one side and the adjacent angles of one are congruent to one side and the adjacent angles of another?

    I am supporse to prove the remaining parts of the image triangle
    land on the target triangle. I am also supposed to restirct my answer to what happens in the plane.

    Is there a way to construct this using compass and straightedge constructions? I am not sure where to start doing this problem. I do not know much about Geometry and proofs. I know we are supposed to carefully draw all the missing diagrams that build the isometry that takes the first triangle into the second, but I am also not sure how to do this.

    Any help would be greatly appreciated!
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  2. #2
    MHF Contributor
    Oct 2009
    Maybe this link can help, though it does not prove the congruence of the triangles from scratch but rather reduces it to SAS. In turn, SAS is discussed in Proposition 4, but ultimately it is taken as an axiom.

    From my recollection, proofs of congruence for triangles are the worst in some sense because they are so close to axioms that it is hard to distinguish something that has to be proved from something taken on faith. Therefore, don't worry if you can't always tell those things apart. Theorems that are studied later may have more complex proofs, but those proofs are more convincing.
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