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Thread: Using Congruent Triangles (Two-Column Proof)

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    Post Using Congruent Triangles (Two-Column Proof)

    In this exercise, there is one piece of unnecessary information. State what information you do not need for the proof. Then give a two-column proof that does not use that piece of information.

    Using Congruent Triangles (Two-Column Proof)-i.png

    Given: LM is congruent to LN; KM is congruent KN; KO bisects MKN; Prove: LO bisects MLN.



    This question is taken from Geometry (McDougal Littell), page 131, question 10 of Written Exercises.
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    Re: Using Congruent Triangles (Two-Column Proof)

    Quote Originally Posted by candaceformosa View Post
    In this exercise, there is one piece of unnecessary information. State what information you do not need for the proof. Then give a two-column proof that does not use that piece of information.
    Click image for larger version. 

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    Given: LM is congruent to LN; KM is congruent KN; KO bisects MKN; Prove: LO bisects MLN.
    You might point out to you teacher that hardly anyone still uses two column proofs.
    Note that $\angle MKO$ is supplementary to $\angle MKL$ AND $\angle NKO$ is supplementary to $\angle NKL$
    So prove that $\Delta MKL\triangleq \Delta NKL$ and you are done.
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    Re: Using Congruent Triangles (Two-Column Proof)

    Quote Originally Posted by candaceformosa View Post
    In this exercise, there is one piece of unnecessary information. State what information you do not need for the proof.


    Click image for larger version. 

Name:	i.PNG 
Views:	5 
Size:	61.0 KB 
ID:	38177

    Given: LM is congruent to LN; KM is congruent KN; KO bisects MKN; Prove: LO bisects MLN.


    candaceformosa, Side LK is congruent to itself. You then have Triangle MKL is congruent to Triangle NKL by Side-Side-Side.

    Then use information about those congruent triangles to show that Line KO bisects Angle MLN.


    So, the piece of information you will not be using (at least by the route I took) is that Line KO bisects Angle MKN.
    Last edited by greg1313; Oct 10th 2017 at 02:31 PM.
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