Allen WolmerSandy Springs, Georgia, US,

April 29, 2015

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Teacher Resources

- Mathematics > General
- Mathematics > Geometry

- Grade 9
- Grade 10

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Table of Contents

- Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
- Students generalize the criterion for perpendicularity of two segments
- Students state the relationship between previously used formats for equations for lines
- Students recognize parallel and perpendicular lines from slope.
- Parallel Lines in the Coordinate Plane
- Perpendicular Lines in the Coordinate Plane

Teacher Resources

Exercises from Illustrative MathematicsA set of 8 exercises, commentary, and solutions

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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.Teacher and Student versions of full lesson from engageNY

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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.Teacher and Student versions of full lesson from engageNY

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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.”Teacher and Student versions of full lesson from engageNY

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Parallel Lines in the Coordinate PlaneWhat if you wanted to figure out if two lines in a shape were truly parallel? How could you do this? After completing this Concept, you'll be able to use slope to help you to determine whether or not lines are parallel.Lessons, videos, exercises, and text from CK-12.

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Perpendicular Lines in the Coordinate PlaneWhat if you wanted to figure out if two lines in a shape met at right angles? How could you do this? After completing this Concept, you'll be able to use slope to help you determine whether or not lines are perpendicular.Lessons, videos, exercises, and text from CK-12. Additional resources available at this site

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