Write-up #1

06/02/02

Bouncing Barney

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.