Bouncing Barney


Beth Lackey

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, go to GSP and construct a triangle. Label the triangle and choose a point on AB.




Then, construct a line that is parallel to the parallel to the point on AB.

Once Barney reaches (intersects) line BC he walks in a direction that is parallel to that point.


When Barney reaches AC he then walks in a direction  parallel to that point.

Once Barney reaches line AB he turns again and walks in a parallel line.

Once Barney intersects with side BC, he walks in a direction parallel to that line.

Barney reaches side AC and moves in a path parallel to that line. He is happily back to his starting point!

Barney had to walk in six different direction to get back to his original starting point.


Here is my final construction. I am trying to animate a point to show the path Barney took. I’ve still got to figure out how to do this!