Bouncing Barney

By:

Allison Kootsikas

 


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?

 


 

First, I construct a GSP sketch for this problem.  Place 3 points in the sketch.  Next highlight them all and construct segments. 

 


Next, place a point on AC.  Construct a parallel line from AC to AB.

 


Next, draw a parallel line from the point on AB parallel to AC.

 


Now draw a parallel line from the point on BC, parallel to AB.


Continue in this manner until you return to the beginning spot.

 


 

Click here to open a GSP file of the discussion.


Barney will hit each wall two times before returning to the start.