By

Danielle Habeeb

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 let’s construct a GSP sketch. Construct the segments AB, BC, CA to
form a triangle. Place a point on
segment AC and create a line parallel to BC. Create a second point at that intersection and make a
parallel line to AC. Create a
third point, and a line parallel to AB.
Use the fourth point to create a parallel line to BC. Take the next point and create a
parallel line to AC. Use the last
point to create a line parallel to AB.
This should complete the path.