In this lesson, students build on their work with parallel and perpendicular lines to prove that non-vertical and non-horizontal perpendicular lines have slopes with opposite reciprocals. Two numbers are reciprocals when their product is 1. The slopes of non-vertical and non-horizontal perpendicular lines are opposite reciprocals because their product is -1. Students begin by rotating a figure 90 degrees. Then they make observations about the slopes of the perpendicular lines in the original figure and the rotated image. They use their observations to make a conjecture about slopes of perpendicular lines. Finally, they have an opportunity to construct a viable argument (MP3) by proving that their conjecture is true for all lines.

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.