Question 2a

By Krista Floer

Will Barney always travel the same distance?

At first I was not sure if Barney always traveled the same distance. I did not think he did before I did some investigating. Before trying to come up with a proof, I want to know if my conjecture is even based in truth. So I measured every side of Barney's path to see if it summed to a magic number like Pi or the golden ratio.

Sadly, it did not. But I did see that if I changed the starting point, the sum did NOT change. So it did sum to a magic number; the perimeter of the triangle ABC. That got me thinking that maybe I could do this proof after all.

Now that we have shown the corner triangles are congruent, we want to show that the inner triangles are congruent. .
Congruent segments have been made the same color to make the proof easier to follow.