Fold Up a Perpendicular
 Topic Index | Algebra Index | Regents Exam Prep Center

This activity is a good warm-up to the study of the slopes of perpendicular lines.

Supplies:  Graph paper, protractors, rulers, (scissors - optional)
                     Overhead projector to display sample graphs, or display enlarged copies on a
                        project size white board, on poster board or on a geoboard. 
                     Display three (or four) graphs where the slopes vary, such as those shown 
                        below.  You can copy these graphs, draw your own graphs, produce graphs
                        using your graphing calculator, or copy graphs from a book.  Notice that
                        these graphs are of segments.

                    

   
         

 A visit from Ski Bird would be appropriate during this activity to reinforce positive versus negative slopes.

 
Directions:  with scissors
This activity can be done in groups or individually.  If done in groups, have EACH student prepare a graph.  The group is for sharing supplies.

Each student copies a different sample graph onto graph paper.

Cut the graph paper so that one of the endpoints is on the edge of the graph paper.

Find the slope of the segment.

Fold the graph paper so that the endpoints of the segment meets.

Unfold the graph paper.  Trace the folded line.  Find its slope.

Measure the angle between the original segment and the folded line.

Record the group's findings to show the slope of each segment and the slope of its fold line.

Make a conjecture about the slopes of perpendicular lines.
 
Directions:  without scissors
If you would rather not use scissors (or scissors are not available), prepare a set of small graphs to hand out.  Place 4 to 6 graph grids on a sheet of paper with one endpoint of the segment already on the edge of the graph.   Reproduce the sheet so that enough grids will be available for each student in the class.  Use a paper cutter to cut out the graphs.  Now your students are ready to fold, measure and work with slopes.
                      

 (Adaptation from a problem in Integrated Mathematics 2 by McDougal Littell)