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Math Help - triangle 2 column proof problem

  1. #1
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    triangle 2 column proof problem

    Hello! I have a problem for school involving 2 column proof that I am close to solving, but can't seem to figure out entirely.

    it's triangle ABC bisected by line BD
    Given line BD is the perpendicular bisector of line AC, Prove line BD bisects angle ABC

    this is what I put:
    Step 1 Line BD is the perpendicular bisector of line AC

    Step 1 Given

    Step 2 Line D is the midpoint of line AC



    Step 2 Definition of a perpendicular bisector

    Step 3 Line segment AD and line segment CD are congruent

    Step 3 Definition of midpoint

    Step 4 Line BD is perpendicular to line AC



    Step 4 Definition of a perpendicular bisector.

    Step 5 Angle ADB and CDB are right angles



    Step 5 Because they are on perpendicular lines

    Step 6 Angle ADB and CDB are congruent




    Step 6 Right angles are always congruent

    Step 7 Line BD is congruent to itself




    Step 7 Reflexive property

    Step 8 Line BD bisects angle ABC
    Step 8 A bisector is a line which runs through the vertex of an angle and divides the angle into two congruent angles


    my grader wrote back that "The proof is easy to follow and contains many logical steps and reasons. Revision of the last step and reasoning is needed to provide a sound logical conclusion. Congruence of triangles is mentioned but has not been clearly established."

    Is anyone able to explain to me where I messed up with this? I thought I did it correctly, and I'm racking my brain here!
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  2. #2
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    Re: triangle 2 column proof problem

    You have just proved the congruence. Look for SAS criterion.
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  3. #3
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    Re: triangle 2 column proof problem

    Doesn't the right angle theorem cover that though?
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