Lesson Plan: Slopes of Parallel and Perpendicular Lines Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use the concept of slopes to determine whether two lines are parallel or perpendicular and use these geometric relationships to solve problems.

Objectives

Students will be able to

  • understand that the slope of a line can be related to the angle the line makes with the positive 𝑥-axis,
  • classify the slope of a line as positive, negative, 0, or infinity when given the (positive or negative) angle the line makes with the positive 𝑥-axis
    • algebraically,
    • graphically (by visually identifying angles as acute, obtuse, right, or equal to zero),
  • find the slope of a line using the the tangent function when given the (positive or negative) angle the line makes with the positive 𝑥-axis,
  • understand the relationship between the slopes of parallel and perpendicular lines,
  • identify whether two given lines are parallel, perpendicular, or neither when given
    • the slopes of the lines,
    • a pair of points that lie on each line,
    • the (positive or negative) angles between the lines and the positive 𝑥-axis,
    • a mixture of the above information allowing the slopes of both lines to be found,
  • use the relationship between the slopes of parallel and perpendicular lines to find
    • an unknown slope of a line,
    • unknown values in the coordinates of a point that lies on a line,
    • an unknown angle between a line and the positive 𝑥-axis.

Prerequisites

Students should already be familiar with

  • coordinates,
  • finding the slope of a line through two points,
  • categorizing the slope of a line as positive, negative, zero, or undefined when given a graph of the line,
  • basic trigonometry.

Exclusions

Students will not cover

  • the equation of a line (in any form),
  • the slopes of straight lines when given arbitrary angles between the lines (angles that are not equal to 90 degrees).

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