Concept 8: Parallel & Perpendicular Slopes
Concept 8: Parallel & Perpendicular SlopesLevel 21. Watch the video (Parallel & Perpendicular Slopes: Level 2)2. Complete the Notes & Basic Practice3. Complete 2 of the following tasksIXL PracticeWorksheetsS18 – (Algebra 1)(at least to 85)Parallel SlopesLevel 24. Take the Schoology Quiz (Concept 8: Level 2)Score of 4 or higher move to level 3Score of 3 or less, complete the Level 2 ReviewLevel 31. Watch the video (Parallel & Perpendicular Slopes: Level 3)2. Complete the Notes & Basic Practice3. Complete 2 of the following tasksIXL PracticeWorksheetsS19 – (Algebra 1)(at least to 85)Parallel & Perpendicular SlopesLevel 34. Take the Schoology Quiz (Concept 8 – Level 3)Score of 3 or less, complete the Level 3 ReviewScore of 4 or higher congratulations, move on to level 4!Level 41. Watch the video (Parallel & Perpendicular Slopes: Level 4)2. Complete the Notes & Basic Practice3. Complete 2 of the following tasksIXL PracticeWorksheetsE6 – (Geometry)Parallel & Perpendicular Slopes(at least to 85)Level 44. Take the Schoology Quiz (Concept 8 – Level 4)Score of 3 or less, complete the Level 2 ReviewScore of 4 or higher congratulations, you are a Math Master!QuizScoresPre-Quiz Score /5Score 5 Level 4Score 3,4 Level 3Score 0-2 Level 2CreatingCreate a graph usingwww.desmos.com of 10 parallellines. Take a screenshot of thegraph, upload it to google driveand share it with me.Level 2Quiz Score:CreatingCreate a graph usingwww.desmos.com of 4 sets ofparallel and perpendicular linesShare the graph with me usinggoogle driveLevel 3Quiz Score:CreatingCreate a graph with a rectanglemade from 4 equationsProveLevel 4Quiz Score:
Level 2/3:Goals:I have mastered level 2 when I can:Identify Parallel Slopes from a Graph and EquationCreate a parallel equation given an equation or graphI have mastered level 3 when I can:Identify Perpendicular Slopes from a Graph and EquationCreate a Perpendicular equation given an equation or graphNotes:Big IdeasExamples ofParallelEquations & GraphsSlopes areParallel when Examples ofPerpendicularEquations & GraphsSlopes arePerpendicular when Examples/Details
Level 2 Practice:For each graph below, write an equation for a parallel line.Level 3 Practice:Find a slope that is perpendicularFor each equation belowFind a slope that is perpendicular to the line that goes througheach of the two points below.For each graph below, write an equation for a perpendicular line.
Worksheet Level 2: Parallel & PerpendicularGoals:I have mastered level 2 when I can:Identify Parallel Slopes from a Graph and EquationCreate a parallel equation given an equation or graphPractice #1
Practice #2Find the equations of lines A, B and C.ABCEquations of the RED, BROWN, GREEN lines.RedBrownGreenQuestionsWhich line is parallel to line A? Write out the slopes of the two equations.Find the equations of RED, BROWN and GREEN lines.Which line is parallel to line B? Write out the slopes of the two equations.Which line is parallel to line C? Write out the slopes of the two equations.What do you notice about slopes of parallel lines?
Worksheet Level 3: Parallel & PerpendicularGoals:I have mastered level 3 when I can:Identify Perpendicular Slopes from a Graph and EquationCreate a Perpendicular equation given an equation or graphPractice #1For each equation below, find the slope and y-intercept.Then find an equation that is parallel and an equation that is tionPerpendicularEquationPractice #2Create an equation for a perpendicular line that passes through the given point on the graph.
Practice #3Find the equations of lines A, B and C.ABCEquations of the BLUE, PURPLE, & ORANGE lines.BluePurpleOrangeQuestionsWhich line is perpendicular to line A? Write out the slopes of the two equations.Find the equations of RED, BROWN and GREEN lines.Which line is perpendicular to line B? Write out the slopes of the two equations.Which line is perpendicular to line C? Write out the slopes of the two equations.What do you notice about slopes of perpendicular lines?
Level 4:Goals:I have mastered level 4 when I can:Create a parallel or perpendicular equation given a slope and a pointAnalyze a polygon using slopesNotes:Big IdeasExamples/Details
Basic Practice:Determine if each shape below is a rectangle by checking the slopes of each side.(Remember rectangles have 4 right angles.)A (-4,0)C (3,-3)B (1,2)D (-2, -5)K (-2,3)N (-3,-2)L (4,2)M (3,-3)
Worksheet Level 4: Parallel & PerpendicularGoals:I have mastered level 4 when I can:Create a parallel or perpendicular equation given a slope and a pointAnalyze a polygon using slopesPractice #1Create an equation for a parallel line and a perpendicular line that passes through the given pointon the graph.Original EquationParallel EquationPerpendicular EquationsOriginal EquationParallel EquationPerpendicular Equations
Practice #21. Plot each set of points on the graphs below.2. Find the slopes of each side.3. Name each polygon based whether or not the sides are parallel or perpendicular or neither.Slopes of the Four SidesSlopes of the Four SidesSlopes of the Four SidesShape:Shape:Shape:Slopes of the Four SidesSlopes of the Four SidesSlopes of the Four SidesShape:Shape:Shape:
IXL Practice Worksheets Creating S18 – (Algebra 1) (at least to 85) Parallel Slopes Level 2 Create a graph using www.desmos.com of 10 parallel lines. Take a screenshot of the graph, upload it to google drive and share it with me. 4. Take the Schoology Quiz (Concept 8: Level 2) Score of
Any two vertical lines are parallel. Postulate 18 Slopes of Perpendicular Lines In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1. The slopes of the two lines that are perpendicular are negative reciprocals of each other. Horizontal lines are perpendicular to vertical lines
perpendicular lines. . .And Why To write an equation that models part of a leaded glass window, as in Example 6 3-7 11 Slope and Parallel Lines Key Concepts Summary Slopes of Parallel Lines If two nonvertical lines are parallel, their slopes are equal. If the slopes of two distinct nonvertical lines are equal, the lines are parallel.
Step 1 Find an equation of a line perpendicular to the two parallel lines. The slopes of the two parallel lines are both 1 — . Use the Slopes of Perpendicular Lines 2 Theorem. 1 — 2 m 1 The product of the slopes of lines is 1. m 2 Multiply each side by 2. Any line with a slope of 2 is perpendicular to the two .
Slopes of Parallel and Perpendicular Lines Example 4A: Writing Equations of Parallel and Perpendicular Lines Write an equation in slope-intercept form for the line that passes through (4, 10) and is parallel to the line described by y 3x 8. Step 1 Find the slope of the line. y 3x 8
a. Parallel to . b. Perpendicular to . c. Parallel to . d. Perpendicular to . 2. Write the equation of the line through @ A and: a. Parallel to . b. Perpendicular to . c. Parallel to . d. Perpendicular to . 3. A vacuum robot is in a room and charging at position . Once charged, it begins moving on a northeast path at
All vertical lines are parallel. Notes: Perpendicular Lines and Slopes Two lines in the same plane that intersect to form right angles are perpendicular lines. Nonvertical lines are perpendicular if and only if their slopes are negative reciprocals. Vertical lines are perpendicular to horizontal lines. Notes: x y 2 4 2 2 2 y 2x 2 y .
This means the lines are neither parallel nor perpendicular. So the answer is neither. Now that we have a sense of how the slopes of parallel and perpendicular lines are related, let’s try some more challenging examples which combine the ideas of 6.5 with parallel and perpendicular lines. Example 3:
3 Parallel and Perpendicular Lines Mathematical Thinking: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. 3.1 Pairs of Lines and Angles 3.2 Parallel Lines and Transversals 3.3 Proofs with Parallel Lines 3.4 Proofs with Perpendicular Lines 3.5 Slopes of Lines 3.6 Equations of Parallel and .
