More Precise Definitions of Parallel and Perpendicular

By Marilyn Mears on Apr 24, 2017

This lesson uses algebra to prove that given lines are parallel or perpendicular.  It also gives students a more precise definition of parallel and perpendicular.

Students will use slope to show that 2 lines are parallel or perpendicular.

 

  • Students need to use correct Nemeth symbols for parallel ( ed L) and  for perpendicular (ed P)

Materials

  • Teacher could present a simple street map and ask students to find a street perpendicular or parallel to a given street. 

Procedure

  1. Using magnetic strips on a white board have students show parallel lines and give their definition.  Then show perpendicular lines and give definition.  
  2. Now students will work on a more precise definition. Plot these equations on a graph board, braille/black lined graph paper, or on the Orion TI-84 Plus Talking Graphing Calculator.

  a.  y = 2x + 3

                  y = 2x - 6

  b.  Have students tell if these lines are parallel or perpendicular and explain their answers.  

            c.   Now plot these equations:  y = 2x + 3 and y = -1/2x + 6

            d.  Have students tell if these lines are parallel or perpendicular and explain their answers.   If using a paper graph, use a  print or braille protractor to measure the angles where the lines intersect. 

            e.  Find the slope for all equations.  Have students tell what they notice about the slopes of the parallel lines and then about the perpendicular lines.

            f.   Add this to the definition of parallel and perpendicular lines.  Parallel lines have the same slope.  Perpendicular lines have slopes which are negative reciprocals.  

Collage of parallel and perpendicular lines