# similar triangles

• Oct 30th 2010, 01:27 PM
gerard54
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
• Oct 30th 2010, 01:57 PM
pickslides
There are similar because each side of the black triangle is bisected by the red triangle evenly.
• Oct 30th 2010, 02:25 PM
gerard54
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?
• Oct 30th 2010, 02:37 PM
Plato
http://www.mathhelpforum.com/math-he...les-triangles.Attachment 19535
Quote:

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

• Oct 30th 2010, 02:38 PM
gerard54
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!!
• Oct 30th 2010, 02:50 PM
Plato