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Thread: Complete the following proof.

  1. #1
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    Complete the following proof.

    Complete the following proof.
    Prove: In an equilateral triangle the three medians are equal.
    Complete the following proof.-q415a.gif
    this is what i have so far
    Complete the following proof.-554e5fd6e4b0dc09b28d163d-valerie709-1431284573062-capture.png
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  2. #2
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    Re: Complete the following proof.

    The rotational symmetry of the triangle give you the result, doesn't it?
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  3. #3
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    Re: Complete the following proof.

    I think the easiest proof is via geometry; prove triangles ABQ, ABR and APC are all congruent with corresponding sides the medians. Actually, I think you used geometry to correctly assign the x-coordinate of C to be a. However, your analytic geometry proof is also easy:

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  4. #4
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    Re: Complete the following proof.

    A classical geometrical proof is sufficient.
    [In what follows, ▲ denotes "triangle"; ∟ denotes "angle"].

    Consider ▲s ARB, AQB
    ∟ARB = ∟AQB = 90
    AB is common to both ▲s
    Since AC = BC and BR and AQ are medians, AR = BQ.
    Thus: ▲ARB & ▲AQB are congruent.
    Hence, AQ = BR

    Repeat that argument for ▲ARB and ▲BRC.
    Result: AQ = BP = BR . . . . as required.

    Al. (Skywave) / June 16, 2017
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