Bouncing Barney Write-up

by

Martha Burns

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 ABC and choose a point on segment AC.  Label that point D.

Construct a line segment from Point D to a point on segment AB parallel to segment BC and label that point E.

Construct a line segment from Point E to a point on segment BC parallel to segment AC and label that point F.

Construct a line segment from Point F to a point on segment AC parallel to segment AC and label that point J.

Construct a line segment from Point J to a point on segment AB parallel to segment BC and label that point K.

Construct a line segment from Point K to a point on segment BC parallel to segment AC and label that point L.

Construct a line segment from Point L to a point on segment AC parallel to segment AB and notice that you return to point D, the starting point.

Barney will touch a wall 6 times before returning to his starting point.