Geometry 3-8 Complete Lesson: Slopes of Parallel and Perpendicular Lines

Last updated about 4 years ago

25 questions

Note from the author:

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Library

Geometry 3-8 Complete Lesson: Slopes of Parallel and Perpendicular Lines

Last updated about 4 years ago

25 questions

Note from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

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Explain.

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Take Note: What do you know about the slopes of parallel lines? Sketch an example pair of parallel lines on the canvas.

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Take Note: What do you know about the slopes of perpendicular lines? Sketch an example pair of perpendicular lines on the canvas.

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Take Note: Summarize the process for determining if two lines are perpendicular from the equations of the lines.

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For each set of points below, line AB contains points A and B. Line CD contains points C and D. Are Line AB and line CD parallel, perpendicular, or neither?

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Error Analysis: Your classmate tries to find an equation for a line parallel to y = 3x - 5 that contains (-4, 2). What is your classmate's error?

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Compare and Contrast: What are the differences between the equations of parallel lines and the equations of perpendicular lines?

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Draggable item		Corresponding Item

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Reflect: Math Success

G.GPE.5

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

10

G.GPE.5

10

Explain.

G.GPE.5

10

Take Note: What do you know about the slopes of parallel lines? Sketch an example pair of parallel lines on the canvas.

10

Take Note: If a line has a slope of 5, what is the slope of a line that is parallel to it? Enter only a number.

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G.GPE.5

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Take Note: What do you know about the slopes of perpendicular lines? Sketch an example pair of perpendicular lines on the canvas.

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Take Note: If a line has a slope of 5, what is the slope of a line that is perpendicular to it? Enter only a simplified fraction.

10

G.GPE.5

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Take Note: Summarize the process for determining if two lines are perpendicular from the equations of the lines.

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G.GPE.5

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G.GPE.5

For each set of points below, line AB contains points A and B. Line CD contains points C and D. Are Line AB and line CD parallel, perpendicular, or neither?

A(-8, 3), B(-4, 11), C(-1, 3), D(1, 2)

\overleftrightarrow{AB} and \overleftrightarrow{CD} are __________.

neither parallel nor perpendicular

perpendicular

parallel

A(3, 5), B(2, -1), C(7, -2), D(10, 16)

\overleftrightarrow{AB} and \overleftrightarrow{CD} are __________.

perpendicular

parallel

neither parallel nor perpendicular

A(3, 1), B(4, 1), C(5, 9), D(2, 6)

\overleftrightarrow{AB} and \overleftrightarrow{CD} are __________.

neither parallel nor perpendicular

parallel

perpendicular

What is an equation of the line perpendicular to the line y = -4x + 1 that contains (2, -3)?

y-3=\frac{1}{4}(x+2)

y+3=-4(x-2)

y-3=-4(x+2)

y+3=\frac{1}{4}(x-2)

10

Error Analysis: Your classmate tries to find an equation for a line parallel to y = 3x - 5 that contains (-4, 2). What is your classmate's error?

G.GPE.5

Compare and Contrast: What are the differences between the equations of parallel lines and the equations of perpendicular lines?

Review Lesson 3-7: Write an equation for the line containing the points.

y = 2x + \frac{1}{2}

y = -x + 6

y = -\frac{1}{2}x + 3

y = -3x + 2

Review Lessons 1-5 and 2-6: Categorize each diagram on the left based on whether ∠1 and ∠2 are congruent.

∠1 and ∠2 are congruent
∠1 and ∠2 are NOT congruent

Vocabulary Review: Use the diagram below to complete each statement on the right with either parallel or perpendicular from the left.

parallel
perpendicular

Line b is __?__ to line a.
Line b is __?__ to the x-axis.
Line a is __?__ to the y-axis.
The x-axis is __?__ to the y-axis.

Vocabulary Review: Consider the conditional statement below and categorize each of the items.

If a polygon is a triangle, then the sum of the measures of its angles is 180.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

a polygon is a triangle
If the sum of the measures of the angles of a polygon is not 180, then the polygon is not a triangle.
If the sum of the measures of the angles of a polygon is 180, then the polygon is a triangle.
the sum of the measures of its angles is 180
If a polygon is not a triangle, then the sum of the measures of its angles is not 180.

Hypothesis
Conclusion
Converse
Inverse
Contrapositive

Use Your Vocabulary: Match each incomplete statement on the left with the word on the right that correctly completes it.

Draggable item		Corresponding Item
The __?__ of \frac{2}{3} is \frac{3}{2}.		reciprocate (VERB)
The blade in the __?__ saw moved back and forth as it cut through the iron.		reciprocal (NOUN)
After your friend helps you with you homework, you __?__ by helping your friend with his chores.		reciprocating (ADJECTIVE)

Reflect: Math Success

Solve It! You and a friend enjoy exercising together. One day, you are about to go running when your friend receives a phone call. You decide to start running and tell your friend to catch up after the call. The red line represents you and the blue line represents your friend. Will your friend catch up?

Yes.

No.

Take Note: If a line has a slope of 5, what is the slope of a line that is parallel to it? Enter only a number.

Problem 1 Got It?

A

B

C

D

Take Note: If a line has a slope of 5, what is the slope of a line that is perpendicular to it? Enter only a simplified fraction.

Problem 2 Got It?

A

B

C

D

Problem 3 Got It? If a given line has a slope of 2, what is the slope of a perpendicular line?

-2

Undefined

2

-\frac{1}{2}

Problem 3 Got It?

A

B

C

D

Problem 4 Got It?

A

B

C

D

Problem 5 Got It? What is an equation of the line representing the player's path?

y-40=\frac{1}{3}(x-90)

y-90=3(x-40)

y-90=\frac{1}{3}(x-40)

A(-8, 3), B(-4, 11), C(-1, 3), D(1, 2)

\overleftrightarrow{AB} and \overleftrightarrow{CD} are __________.

neither parallel nor perpendicular

perpendicular

parallel

A(3, 5), B(2, -1), C(7, -2), D(10, 16)

\overleftrightarrow{AB} and \overleftrightarrow{CD} are __________.

perpendicular

parallel

neither parallel nor perpendicular

A(3, 1), B(4, 1), C(5, 9), D(2, 6)

\overleftrightarrow{AB}  and \overleftrightarrow{CD} are __________.

neither parallel nor perpendicular

parallel

perpendicular

What is an equation of the line perpendicular to the line y = -4x + 1 that contains (2, -3)?

y-3=\frac{1}{4}(x+2)

y+3=-4(x-2)

y-3=-4(x+2)

y+3=\frac{1}{4}(x-2)

Review Lesson 3-7: Write an equation for the line containing the points.

y = 2x + \frac{1}{2}

y = -x + 6

y = -\frac{1}{2}x + 3

y = -3x + 2

Review Lessons 1-5 and 2-6: Categorize each diagram on the left based on whether ∠1 and ∠2 are congruent.

∠1 and ∠2 are congruent

∠1 and ∠2 are NOT congruent

Vocabulary Review: Use the diagram below to complete each statement on the right with either parallel or perpendicular from the left. 

parallel

perpendicular

Line b is __?__ to line a.

Line b is __?__ to the x-axis.

Line a is __?__ to the y-axis.

The x-axis is __?__ to the y-axis.

Vocabulary Review: Consider the conditional statement below and categorize each of the items.

If a polygon is a triangle, then the sum of the measures of its angles is 180.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it. 

a polygon is a triangle

If the sum of the measures of the angles of a polygon is not 180, then the polygon is not a triangle.

If the sum of the measures of the angles of a polygon is 180, then the polygon is a triangle.

the sum of the measures of its angles is 180

If a polygon is not a triangle, then the sum of the measures of its angles is not 180.

Hypothesis

Conclusion

Converse

Inverse

Contrapositive

Use Your Vocabulary: Match each incomplete statement on the left with the word on the right that correctly completes it.

The __?__ of \frac{2}{3} is \frac{3}{2}.

reciprocate (VERB)

The blade in the __?__ saw moved back and forth as it cut through the iron.

reciprocal (NOUN)

After your friend helps you with you homework, you __?__ by helping your friend with his chores.

reciprocating (ADJECTIVE)

Solve It! You and a friend enjoy exercising together. One day, you are about to go running when your friend receives a phone call. You decide to start running and tell your friend to catch up after the call. The red line represents you and the blue line represents your friend. Will your friend catch up?

Yes.

No.

Problem 1 Got It?

A

B

C

D

Problem 2 Got It?

A

B

C

D

Problem 3 Got It? If a given line has a slope of 2, what is the slope of a perpendicular line?

-2

Undefined

2

-\frac{1}{2}

Problem 3 Got It?

A

B

C

D

Problem 4 Got It?

A

B

C

D

Problem 5 Got It? What is an equation of the line representing the player's path?

y-40=\frac{1}{3}(x-90)

y-90=3(x-40)

y-90=\frac{1}{3}(x-40)

Geometry 3-8 Complete Lesson: Slopes of Parallel and Perpendicular Lines

Geometry 3-8 Complete Lesson: Slopes of Parallel and Perpendicular Lines

Explain.

Take Note: What do you know about the slopes of parallel lines? Sketch an example pair of parallel lines on the canvas.

Take Note: What do you know about the slopes of perpendicular lines? Sketch an example pair of perpendicular lines on the canvas.

Take Note: Summarize the process for determining if two lines are perpendicular from the equations of the lines.

Error Analysis: Your classmate tries to find an equation for a line parallel to y = 3x - 5 that contains (-4, 2). What is your classmate's error?

Compare and Contrast: What are the differences between the equations of parallel lines and the equations of perpendicular lines?

Reflect: Math Success

Explain.

Take Note: What do you know about the slopes of parallel lines? Sketch an example pair of parallel lines on the canvas.

Take Note: If a line has a slope of 5, what is the slope of a line that is parallel to it? Enter only a number.

Take Note: What do you know about the slopes of perpendicular lines? Sketch an example pair of perpendicular lines on the canvas.

Take Note: If a line has a slope of 5, what is the slope of a line that is perpendicular to it? Enter only a simplified fraction.

Take Note: Summarize the process for determining if two lines are perpendicular from the equations of the lines.

A(-8, 3), B(-4, 11), C(-1, 3), D(1, 2)\overleftrightarrow{AB} and \overleftrightarrow{CD} are __________.

A(3, 5), B(2, -1), C(7, -2), D(10, 16)\overleftrightarrow{AB} and \overleftrightarrow{CD} are __________.

A(3, 1), B(4, 1), C(5, 9), D(2, 6)\overleftrightarrow{AB} and \overleftrightarrow{CD} are __________.

What is an equation of the line perpendicular to the line y = -4x + 1 that contains (2, -3)?

Error Analysis: Your classmate tries to find an equation for a line parallel to y = 3x - 5 that contains (-4, 2). What is your classmate's error?

Compare and Contrast: What are the differences between the equations of parallel lines and the equations of perpendicular lines?

Review Lesson 3-7: Write an equation for the line containing the points.

Review Lessons 1-5 and 2-6: Categorize each diagram on the left based on whether ∠1 and ∠2 are congruent.

Vocabulary Review: Use the diagram below to complete each statement on the right with either parallel or perpendicular from the left.

Use Your Vocabulary: Match each incomplete statement on the left with the word on the right that correctly completes it.

Reflect: Math Success

Take Note: If a line has a slope of 5, what is the slope of a line that is parallel to it? Enter only a number.

Problem 1 Got It?

Take Note: If a line has a slope of 5, what is the slope of a line that is perpendicular to it? Enter only a simplified fraction.

Problem 2 Got It?

Problem 3 Got It? If a given line has a slope of 2, what is the slope of a perpendicular line?

Problem 3 Got It?

Problem 4 Got It?

Problem 5 Got It? What is an equation of the line representing the player's path?

A(-8, 3), B(-4, 11), C(-1, 3), D(1, 2)

\overleftrightarrow{AB} and \overleftrightarrow{CD} are __________.

A(3, 5), B(2, -1), C(7, -2), D(10, 16)

\overleftrightarrow{AB} and \overleftrightarrow{CD} are __________.

A(3, 1), B(4, 1), C(5, 9), D(2, 6)

\overleftrightarrow{AB} and \overleftrightarrow{CD} are __________.