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.

Part b
Part c
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