# Thread: Using Congruent Triangles (Two-Column Proof)

1. ## 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.

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.

2. ## Re: Using Congruent Triangles (Two-Column Proof)

Originally Posted by candaceformosa
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.

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.

3. ## Re: Using Congruent Triangles (Two-Column Proof)

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

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.