1. ## 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

2. There are similar because each side of the black triangle is bisected by the red triangle evenly.

3. 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?

4. Originally Posted by gerard54
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

5. 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!!