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Math Help - Similar triangles

  1. #1
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    Similar triangles

    I have an equillateral triangle and require to calculate the lengths of two parallel lengths.

    I have included a sketch to help identify.

    BC = AB = AC
    YZ AY AZ

    I know;

    AB = 3
    AC = 3
    AY = 2
    AZ = 2

    I require to find the ratios BC and YZ

    AB = AC = BC
    AZ AY YZ

    3 = 3 = x
    2 2 x

    How do I work with this method above to isolate BC and YZ
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  2. #2
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    Re: Similar triangles

    Quote Originally Posted by David Green View Post
    I have an equillateral triangle and require to calculate the lengths of two parallel lengths.
    How do I work with this method above to isolate BC and YZ
    Because \Delta ABC \approx \Delta AYZ\, \Rightarrow \,\frac{{BC}}{{YZ}} = \frac{{BA}}{{YA}}.
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  3. #3
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    Re: Similar triangles

    Quote Originally Posted by Plato View Post
    Because \Delta ABC \approx \Delta AYZ\, \Rightarrow \,\frac{{BC}}{{YZ}} = \frac{{BA}}{{YA}}.
    The problem there is that you have given two unknowns on the LHS, where both cannot be solved at the same time?

    I know the answers, but I don't know how to perform the algebra to solve the lengths of the sides?
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  4. #4
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    Re: Similar triangles

    Quote Originally Posted by David Green View Post
    The problem there is that you have given two unknowns on the LHS, where both cannot be solved at the same time? I know the answers, but I don't know how to perform the algebra to solve the lengths of the sides?
    It is an equilateral triangle: CB=BA=AC
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  5. #5
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    Re: Similar triangles

    Quote Originally Posted by Plato View Post
    It is an equilateral triangle: CB=BA=AC
    I know its an equilateral triangle, and I know each angle is 60 degrees, and I know AB = 3, BC = 3, and AC = 3, and YZ = 2

    I just can't prove it mathematically
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  6. #6
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    Re: Similar triangles

    Quote Originally Posted by David Green View Post
    I know its an equilateral triangle, and I know each angle is 60 degrees, and I know AB = 3, BC = 3, and AC = 3, and YZ = 2

    I just can't prove it mathematically
    It's a given, you don't need to prove it. Unless you've mistyped the question
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  7. #7
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    Re: Similar triangles

    Quote Originally Posted by david green View Post
    i know its an equilateral triangle, and i know each angle is 60 degrees, and i know ab = 3, bc = 3, and ac = 3, and yz = 2
    i just can't prove it mathematically
    Help!
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  8. #8
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    Re: Similar triangles

    Thanks for info.
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