Bouncing Barney

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# Scottie Benford

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?

Construct a triangle using GSP.  Using the construction show the number of times that Barney will reach the wall before he returns to his starting point.

First construct a parallel line from a point on segment AC to segment AB.  Next construct a parallel line from the point on AB to BC that is parallel to AC.  Then construct a parallel line from the point on BC to AC that is parallel to AB.  The next parallel line runs from the point on AC to AB and is parallel to BC.  Construct a parallel line from the point on AB to BC that is parallel to AC. The last parallel line is from the point on BC to the beginning point on AC.  Using the construction we come to the conclusion that Barney will run into the wall six times before he returns to his starting point.  I would now like to show each individual step of Barney’s route.

The last six pictures are a break down of the first picture.  More points and explanation was added for better understanding of the path of Barney.