6.1: Perpendicular Slopes
This activity is intended to supplement Algebra I, Chapter 5, Lesson 4.
ID: 8973
Time required: 45 minutes
Topic: Linear Functions
- Graph lines whose slopes are negative reciprocals and measure the angles to verify they are perpendicular.
Activity Overview
In this activity, students investigate the “negative reciprocal” relationship between the slopes of perpendicular lines. The final phase of the activity is appropriate for more advanced students as they are led through an algebraic proof of the relationship. Optional geometric activities (Problems 5 and 6) use the result to verify that (1) the radius of a circle and its tangent line are perpendicular and (2) a triangle inscribed in a circle with the diameter as one side is a right triangle.
Teacher Preparation
This activity is appropriate for students in Algebra 1. It is assumed that students have recently been introduced to the notion of slope and perhaps the fact that two lines are parallel if and only if they have the same slope.
- To download Cabri Jr. and its files, go to http://www.education.ti.com/calculators/downloads/US/Activities/Detail?id=8973, and select Cabri Jr., PERP1.8xv, PERP2.8xv, PERP3.8xv, PERP4.8xv, PERP5.8xv, and PERP6.8xv. If your calculator already has the Cabri Jr. application, you may still need to download the .8xv files".
Classroom Management
- This activity is designed to have students explore individually and in pairs. However, an alternate approach would be to use the activity in a whole-class format. By using the computer software and the questions found on the student worksheet, you can lead an interactive class discussion on the slope of perpendicular lines.
- This worksheet is intended to guide students through the main ideas of the activity. You may wish to have the class record their answers on a separate sheet of paper, or just use the questions posed to engage a class discussion.
- Information for an optional extension is provided at the end of this activity; information for students is provided in the CabriJr Files PERP5 and PERP6.
Associated Materials
- Student Worksheet: Perpendicular Slopes, http://www.ck12.org/flexr/chapter/9615
- Cabri Jr. Application
- PERP1, PERP2, PERP 3, PERP4, PERP5, PERP6 (Cabri Jr. files)
See the student worksheet for specific directions on how to complete the activity.