By: Shelly Kaufmann
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, construct a GSP sketch for the problem. Draw a triangle ABC. Place a point anywhere on line segment AC. Label the new point D.
From your newly established point D on AC, draw a line segment to AB that is parallel to BC. Label the point E.
From E, draw a line segment to BC that is parallel to AC. Label the point F.
Next, draw a line segment that is parallel to AB from F. The new point should be on segment AC.
From F, draw a line segment that is parallel to AB. Continue the pattern until you are back at starting point D.
From this drawing, you can conclude that he hits the wall 6 times.