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• NC.M1.G-GPE.5 - Use coordinates to prove the slope criteria for parallel and perpendic...
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This task explores the real world topic of building light rails. Throughout the implementation of this task the students will learn about the cost of building railways and how to implement them within a budget. This task explores such mathematical concepts of using coordinates to find the distance between points, using coordinates to build polygons and find the area and length of sides, and writing equations of parallel lines.

Subject:
Algebra
Geometry
Material Type:
Activity/Lab
Author:
Carrie Robledo
James O'Neal
Date Added:
03/26/2021
Unrestricted Use
CC BY
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Equation of a line with image, equations of parallel lines with image, equations of perpendicular lines with image.

Subject:
Geometry
Mathematics
Material Type:
Interactive
Provider:
Michigan Virtual
Date Added:
07/19/2019
Only Sharing Permitted
CC BY-NC-ND
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This lesson unit is intended to help teachers assess how well students are able to understand the relationship between the slopes of parallel and perpendicular lines and, in particular, to help identify students who find it difficult to: find, from their equations, lines that are parallel and perpendicular; and identify and use intercepts. It also aims to encourage discussion on some common misconceptions about equations of lines.

Subject:
Mathematics
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
07/31/2019
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CK-12's Basic Geometry FlexBook is designed to present students with geometric principles in a simpler, more graphics-oriented course. Students will explore geometry at a slower pace with an emphasis placed on visual aids and approachability.

Subject:
Mathematics
Material Type:
Textbook
Provider:
CK-12 Foundation
Provider Set:
CK-12 FlexBook
Author:
Cifarelli, Victor
Farbizio, Annamaria (Editor)
Gloag, Andrew
Greenberg, Dan
Jordan, Lori
Sconyers, Jim
Zahner, Bill
Date Added:
10/11/2010
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Students generalize the criterion for perpendicularity of two segments that meet at a point to any two segments in the Cartesian plane.
Students apply the criterion to determine if two segments are perpendicular.

Subject:
Math 1
Mathematics
Material Type:
Lesson
Author:
EngageNY
Date Added:
02/21/2020
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CC BY-NC-SA
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Students state the relationship between previously used formats for equations for lines and the new format a1x + a2y + c, recognizing the segments from (0,0) to (a1, a2) as a normal and - a2/a1 as a slope.
Students solve problems that are dependent upon making such interpretations.

Subject:
Math 1
Mathematics
Material Type:
Lesson
Author:
EngageNY
Date Added:
02/21/2020
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CC BY-NC-SA
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Students recognize parallel and perpendicular lines from slope.
Students create equations for lines satisfying criteria of the kind: “Contains a given point and is parallel/perpendicular to a given line.”

Subject:
Math 1
Mathematics
Material Type:
Lesson
Author:
EngageNY
Date Added:
02/21/2020
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CC BY-NC-SA
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The challenge of programming robot motion along segments parallel or perpendicular to a given segment leads to an analysis of slopes of parallel and perpendicular lines. Students write equations for parallel, perpendicular, and normal lines. Additionally, students will and study the proportionality of segments formed by diagonals of polygons.

Subject:
Math 1
Mathematics
Material Type:
Lesson
Author:
EngageNY
Date Added:
02/21/2020
Conditional Remix & Share Permitted
CC BY-NC-SA
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In this task students make a conjecture about the slopes of perpendicular lines. This observation will be formally proved in a later task, but the representation-based argument presented in this task suggests that this is a reasonable generalization across all cases. In the previous task, students encountered the idea of perpendicularity when they were asked to rotate the lizard 90°, and they may also have noticed the idea when they considered the relationship between the line of reflection and the points on the reflected image of the lizard. Students might have used the square corner of a piece of paper or a protractor to measure these right angles. In this task they consider how the coordinate grid can be used to determine if two lines are perpendicular. This is one example of the connections that can be made between coordinate geometry and transformations. It is powerful for students to be able to draw upon two different representational systems to think about the same ideas. In this task, students also consider a definition of perpendicular that is related to reflections: Two lines are perpendicular if they meet to form congruent adjacent angles.

Subject:
Math 1
Mathematics
Material Type:
Lesson
Author:
The Mathematics Vision Project
Date Added:
03/10/2020
Unrestricted Use
CC BY
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Image of parallel lines, image of perpendicular lines, and image of intersecting lines, each image followed by text in accordion of properties of eac.n

Subject:
Geometry
Mathematics
Material Type:
Interactive
Provider:
Michigan Virtual
Date Added:
07/19/2019
Unrestricted Use
CC BY
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This is an activity. I like to call it "Making a worksheet more than a worksheet".  This is a musical review. Students will put their name on their paper, pass the paper when the music is playing and when it stops, answer the question they are on.

Subject:
Math 1
Material Type:
Assessment
Author:
KORI ELLIOTT
Date Added:
07/14/2020
Unrestricted Use
CC BY
Rating
0.0 stars

This is an activity. I like to call it "Making a worksheet more than a worksheet".  This is a musical review. Students will put their name on their paper, pass the paper when the music is playing and when it stops, answer the question they are on.

Subject:
Math 1
Material Type:
Lesson Plan
Author:
Danielle Flores
Date Added:
11/06/2019
Read the Fine Print
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In this Khan Academy activity, students will determine if two lines are perpendicular or parallel from their equations.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Khan Academy
Date Added:
08/23/2018
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Khan video developing idea of parallel and perpendicular lines using point on the line.

Subject:
Mathematics
Material Type:
Demonstration
Provider:
Khan Academy
Date Added:
02/28/2018
Read the Fine Print
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In this Khan Academy activity, students will determine if two lines are perpendicular or parallel from their graph.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Khan Academy
Date Added:
08/23/2018
Unrestricted Use
CC BY
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Course presentation slides for each step of proving vertical angles are congruent, using intersecting lines and supplementary angles.

Subject:
Geometry
Mathematics
Material Type:
Interactive
Provider:
Michigan Virtual
Date Added:
07/19/2019
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This video proves why perpendicular lines have slopes that are negative reciprocals.

Subject:
Mathematics
Material Type:
Demonstration
Provider:
Khan Academy
Date Added:
02/28/2018
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The purpose of this task is to prove that parallel lines have equal slopes and that the slopes of perpendicular lines are negative reciprocals. Students have used these theorems previously. The proofs use the ideas of slope triangles, rotations, and translations. Both proofs are preceded by a specific case that demonstrates the idea before students are asked to follow the logic using variables and thinking more generally.

Subject:
Math 1
Mathematics
Material Type:
Lesson
Author:
The Mathematics Vision Project
Date Added:
03/10/2020
Read the Fine Print
Rating
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In this Khan Academy activity, students will write the equations of parallel and perpendicular lines.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Khan Academy
Date Added:
08/23/2018