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Triangle congruent problem

  1. Apr 29, 2007 #1
    In the diagram, AM is a medium of triangle ABC. Perpendicular lines drawn from B and C to AM (or its extension) meet AM at P and Q respectively.

    Prove that BP = CQ

    So far I have concluded that:

    BM = CM
    Angle BPM = angle CQM
    Triangle ABM = ACM

    I am not sure what else I can do in order to prove that the triangles BMP and CMQ are congruent which would prove that BP = CQ

    Attached Files:

    Last edited: Apr 29, 2007
  2. jcsd
  3. Apr 30, 2007 #2


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    Staff Emeritus
    Science Advisor

    Since the lines are drawn perpendicular to AM, you have RIGHT triangles. Further, since M is a "median" (note spelling) BM and CM are congruent.
  4. Apr 30, 2007 #3
    Consider Triangles BMP and CMQ
    You know

    BM = CM (given hypothesis)

    angle BPM = angle CQM as they are both at right angles to AM or its extension

    180 degrees - angle AMC = angle AMB, angle AMB + angle QMB = 180 degrees
    Therefore, angle AMC = angle AMB

    Triangle BMP and CMQ are congruent by the AAS condition of the triangle theorm.

    Therefore, BP = CQ
    Last edited: Apr 30, 2007
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