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

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- October 30th 2010, 01:27 PMgerard54similar 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 - October 30th 2010, 01:57 PMpickslides
There are similar because each side of the black triangle is bisected by the red triangle evenly.

- October 30th 2010, 02:25 PMgerard54
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?

- October 30th 2010, 02:37 PMPlato
- October 30th 2010, 02:38 PMgerard54
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!!

- October 30th 2010, 02:50 PMPlato
Look at my reply.

- October 30th 2010, 02:58 PMgerard54
I think I've got it, thanks guys.