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Math Help - similar triangles

  1. #1
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    similar triangles

    Hello,
    Could someone please explain why the red and black triangles in the attached image
    are similar? I've looked at it over and over and am failing to see something which I'm
    sure should be very basic.
    Thanks for any help.
    Gerard
    Attached Thumbnails Attached Thumbnails similar triangles-triangles.png  
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  2. #2
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    There are similar because each side of the black triangle is bisected by the red triangle evenly.
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  3. #3
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    yes, I'm aware of the bisected lines, but I don't see how that proves the triangles are similar. Is there a standard proof for this problem?
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  4. #4
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    similar triangles-triangles.png
    Quote Originally Posted by gerard54 View Post
    Hello,
    Could someone please explain why the red and black triangles in the attached image
    are similar? I've looked at it over and over and am failing to see something which I'm
    sure should be very basic.
    Thanks for any help.
    Gerard
    Last edited by Plato; October 31st 2010 at 06:23 AM.
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  5. #5
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    Here's a better picture that I've attached. I've discovered that when the bisectors of two sides are joined, the line joining them is parallel to the third side. This makes it easy to form parallelograms, and prove that the sides of the inner triangle are half the length of the sides they're parallel to. Now I just need a proof that shows why the lines are parallel!!
    Attached Thumbnails Attached Thumbnails similar triangles-similartriangles.png  
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  6. #6
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    Look at my reply.
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  7. #7
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    I think I've got it, thanks guys.
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