Polygons and Algebraic Relationships

Lesson 5

Math

Unit 5

10th Grade

Lesson 5 of 15

Objective


Describe and apply the slope criteria for parallel lines.

Common Core Standards


Core Standards

  • G.GPE.B.5 — 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).

Foundational Standards

  • 8.EE.B.6
  • 8.EE.C.8
  • 8.G.A.1
  • A.REI.C.6

Criteria for Success


  1. Identify parallel lines on the coordinate plane by verifying several points along the lines that are the same distance and perpendicular to both lines. 
  2. Describe that parallel lines can be thought of as a system of equations with no solutions. 
  3. Describe that a parallel line is formed through translation and translations result in parallel line segments. 
  4. Apply the knowledge of slope criteria to write equations of the lines that are parallel to a given line through a point. 
  5. Identify equations of parallel lines without graphing. 

Tips for Teachers


  • In this lesson, we are preparing for the identification of quadrilaterals based on perpendicular and parallel criteria. This goes back to a fourth-grade geometry standard: 4.G.2 “Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines.” We will not get into more properties of parallelograms specifically or quadrilaterals generally in this lesson. 
  • This lesson mirrors Lesson 4 but with a focus on parallel lines.
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Anchor Problems

25-30 minutes


Problem 1

In the diagram below, $${m\parallel p}$$.

a. Write three equations that are perpendicular to line $$m$$

b. What is the relationship between your three equations and line $$p$$?

c. Find the distance between line $$m$$ and $$p$$ using your three equations. What do you notice? 

Guiding Questions

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References

CK-12 Distance between Parallel Lines

Distance between Parallel Lines is made available by CK-12 under the CC BY-NC 3.0 license. © CK-12 Foundation 2017. Visit them at ck12.org. Accessed June 1, 2018, 4:27 p.m..

Problem 2

In the diagram below, $${\overleftrightarrow {AI} \parallel {\overleftrightarrow {CK}}}$$ and $${\overleftrightarrow{IC} \perp \overleftrightarrow {AK}}$$. How can you use the triangles $${AHI}$$ and $${KHC}$$ to prove that the slopes for $${\overleftrightarrow{AI}}$$ and $${\overleftrightarrow {CK}}$$ are the same?

Guiding Questions

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Problem 3

Write three equations that are parellel to $${\overleftrightarrow{AB}}$$.

Guiding Questions

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Target Task

5-10 minutes


Write the equation of the line that passes through point $${ (6,8)}$$ and is parallel to the line $${3x+2y=8}$$.

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems where students must write equations for lines that are parallel to a given line and pass through a given point.
  • Include problems such as “There is a line $${{\overleftrightarrow{CD}}}$$  that is intersected at a right angle by line $${{\overleftrightarrow{GH}}}$$. Three other lines are drawn so they are also perpendicular to $${{\overleftrightarrow{CD}}}$$. What do you know about the relationship of these lines to $${{\overleftrightarrow{GH}}}$$?”

Next

Identify and create parallelograms, rectangles, rhombuses, and squares on the coordinate plane.

Lesson 6
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Distance on the Coordinate Plane

Topic B: Classify Polygons using Slope Criteria and Proportional Line Segments

Topic C: Area and Perimeter On and Off the Coordinate Plane

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