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Math Help - Isosceles Triangle Proof

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    Isosceles Triangle Proof

    Prove that a triangle is isosceles if and only if two medians are congruent.
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    The basic idea behind this proof is that in two right triangles if the hypotenuses are congruent and two legs are congruent then the triangles are congruent.
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    I was able to use that idea to prove that a triangle is isosceles iff its altitudes are congruent but medians? What hypotenuse? I am having trouble with the part of the proof where I am assuming that the medians are congruent.
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    A different approach involves the fact that the centroid divides any median in the ratio 2:1. Suppose in triangle ABC, the medians AD and BE are equal and intersect at centroid G. Can you use the fact above to prove something about triangles AGE and BGD ?
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    isosce les triangle proof

    posted by MATNTRNG
    1 atriangleABC has a base BC and two rays AB andAC. midpoints of AB=M of AC =N
    2 BN = CM given
    3 MN is parallel to BC ( similar triangles )
    4 arcs are drawn at B and C of equal lenghts ( median lenght)
    5 a line parallel to BC is drawn above BC meeting arcs at M and N
    6 MNCB is a trapezoid
    7BN and CM are the trapezoid diagonals which are equal 4 above
    8 MNCB is a regular trapezoid
    9 a regular trapezoid is a truncated isosceles triangle
    BM and CM extended meet at A the apex of isoscelesABC


    bjh
    Last edited by bjhopper; October 1st 2010 at 04:28 PM. Reason: correct mistake
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