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Math Help - Altitudes and Medians

  1. #1
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    Altitudes and Medians

    Hi guys,

    So I had a question about altitudes and medians. If two altitudes of a triangle are congruent to each other, then the medians of the corresponding sides are also congruent. Is this statement always true or is there an exception?

    Thanks - blahblahblah1234
    Last edited by blahblahblah1234; October 22nd 2011 at 10:04 AM. Reason: The problem is solved.
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  2. #2
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    Re: Altitudes and Medians

    Quote Originally Posted by blahblahblah1234 View Post
    Hi guys,

    So I had a question about altitudes and medians. If two altitudes of a triangle are congruent to each other, then the medians of the corresponding sides are also congruent. Is this statement always true or is there an exception?

    Thanks - blahblahblah1234
    note that the area of a triangle is A = \frac{1}{2}bh

    if h is an altitude, then b is the side perpendicular to that altitude

    so ...

    \frac{1}{2} b_1 h_1 = \frac{1}{2} b_2 h_2

    if h_1 = h_2 , what does that say about the lengths of the two corresponding sides, b_1 and b_2 ?

    further ... what kind of triangle would this be, and what can you say about the lengths of the medians to these two corresponding sides?
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  3. #3
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    Re: Altitudes and Medians

    Thanks skeeter, haha. Soo the triange would be isoceles or equilateral and the medians would be congruent to the altitudes. Thanks again.
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