Bouncing Barney

Write Up

By: Diane Swaney

 

 

Barney is in the triangular room shown here. He walks from a point on AC parallel to BC. When he reaches AB, he turns and walks parallel to AC. When he reaches BC, he turns and walks parallel to AB. How many times will Barney reach a wall before returning to his starting point?

 

 

(Source: Adapted from Mathematics Teaching in the Middle School).

 

First: Let’s construct a GSP sketch

 

 

If Barney starts at a point on AC  (point D) and walks in a straight line that is parallel to line segment BC (line segment DE), then he turns and walks parallel to line segment AC (line segment EF), he turns and walks parallel to BA and continues in this pattern.  It would take two complete circuits of bouncing off the side of the triangle to make it back to Barney’s starting point.