Bouncing Barney


Linda LaPerre


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?








If D is the first point and you construct a line parallel to BC,  the new line intersects AB at point E.  Contruct a line from point E that is parallel to AC.  The intersecting point is at point F.  Construct a line from point F that is parallel to AB.  The new intersecting point created is G.  Continue this process and create points H and I.  When the last parallel line is formed from I, you will return to D.  It takes two complete trips around to get back to the original point.


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