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Slopes of perpendicular lines

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Slopes of Perpendicular Lines

Slopes of Perpendicular Lines

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• 1. perpendicular lines &#x2013; In a plane, any two oblique lines theproduct of whose slopes is -1.Slopes of Perpendicular LinesRemember Slope-Intercept Form of a Line?y = mx + bm = slope (rise over run)b = y-intercepty = mx + b
• 2. Are these lines perpendicular?PullPull
• 3. Are the following slopes perpendicular?Slopes Perpendicular?No, the slopes have opposite signs, butare not reciprocals.Are the following lines are perpendicular?y = 4x + 2 y = &#x2013;4x &#x2013; 2m1 = 4 m2 = &#x2013;4AnswerSlope of Line 2Slope of Line 1
• 4. Are the following lines are perpendicular?Yes, the slopes are opposite reciprocals.AnswerSlope of Line 2Slope of Line 1Are the following lines are perpendicular?Yes, the slopes are opposite reciprocals. They-intercept is not important for perpendicularityAnswerSlope of Line 2Slope of Line 1
• 5. Are the following lines are perpendicular?No, the slopes are reciprocals, but do not haveopposite signs. AnswerSlope of Line 1 Slope of Line 2Original Slope Perpendicular SlopeFind the Perpendicular Slope
• 6. Now that we have defined perpendicular lines, find fiveexamples of perpendicular lines in the classroom. For eachexample, explain why it is important that the lines areperpendicular, if it is not important, explain why not.Lesson objectives Teachers notes1) Learn the definition of perpendicular lines2) Determine whether the slopes of two lines are perpendicular.3) Determine whether two lines in slope-intercept form areperpendicular.4) Find the perpendicular slope to a given slope.Slopes ofPerpendicular Lines
• 7. Teachers notesLesson objectivesSubject:Topic:Grade(s):Prior knowledge:Cross-curricular link(s):MathematicsPerpendicular SlopeAlgebra 1 or Algebra 2Slope-Intercept Form of a line. Findingslope of a line given its graph.Find perpendicular lines in the classroom.Lesson notes:Next PageCommon Core Standard - G.GPE.5 Prove the slope criteria for parallel andperpendicular lines and use them to solve geometric problems (e.g., find the equationof a line parallel or perpendicular to a given line that passes through a given point).Teachers notesLesson objectivesLesson notes (continued):1) The books definition of perpendicular lines is given. Redefine after student discovery.2) Refresh student memory on Slope-Intercept Form. Stress that m &amp; b are independent.3) Refresh student memory on graphs of lines. Refresh memory on how to count slope.4) Use the protractor to show that lines are perpendicular. Lead students on a discovery ofwhat perpendicular pairs look like.5) Have students determine why or why not pairs represent perpendicular slopes.6-9) Have students find the slopes of both lines and determine why or why not the lines areperpendicular. Stress that the y-intercepts are not important for this determination.10) Have students find the perpendicular pair given an original slope.11) Have students find examples of perpendicular lines in the classroom. Have the studentsdetermine why or why not the examples need to be perpendicular.Previous PagePage(s) Associated NotesNext Page
• 8. Teachers notesLesson objectivesLesson notes (continued):Previous PageSource CreditsPage 1 - definition from "Algebra 2" by Holliday, et. at., Glencoe, 2005.Page 3 - Interactive software from Smart Technologies Smart Notebook 10.Page 4 - Graphics and protractor from Smart Technologies Smart Notebook 10.