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Math Help - Geometrical Proof Question Help

  1. #1
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    Geometrical Proof Question Help

    I am a grade 9 student, and I need help to understand how to solve these two questions. Thanks in Advance!
    Also ignore the writing on the paper, it was my friends

    Geometrical Proof Question Help-10249005_299652760192385_1704314297_n.jpg
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  2. #2
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    Re: Geometrical Proof Question Help

    For the 2nd problem

    from the 2 right triangles you are told exist, using the pythagorean theorem

    $x^2 + h^2 = a^2$

    $y^2 + h^2 = b^2$

    now you are told that $h^2 = x y$

    substituting this in we get

    $x^2 + xy = a^2$

    $y^2 + xy = b^2$

    adding these two equations we get

    $x^2 + y^2 + 2 x y = a^2 + b^2$

    $(x+y)^2 = a^2 + b^2$

    and looking at triangle ACB we see that $x+y$ is the hypotenuse of the triangle with legs $a$ and $b$ and as

    $(x+y)^2 = a^2 + b^2$ ACB must be a right triangle.
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  3. #3
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    Re: Geometrical Proof Question Help

    Quote Originally Posted by pan7331 View Post
    I am a grade 9 student, and I need help to understand how to solve these two questions. Thanks in Advance!
    Also ignore the writing on the paper, it was my friends

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    for the first one just look at the right triangles caused by the fact that $BD \bot AB$ and use the pythagorean theorem.
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  4. #4
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    Re: Geometrical Proof Question Help

    Thanks your help! Much appreciated
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