Curriculum  /  Math  /  10th Grade  /  Unit 5: Polygons and Algebraic Relationships  /  Lesson 4

Polygons and Algebraic Relationships

Lesson 4

Math

Unit 5

10th Grade

Lesson 4 of 15

Objective

Algebraically and using the Pythagorean Theorem, determine the slope criteria for perpendicular 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).
  • G.SRT.C.8 — Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.

Foundational Standards

  • 8.EE.B.6
  • 8.G.B.6

Criteria for Success

  1. Identify right triangles on the coordinate plane using the Pythagorean Theorem. 
  2. Describe the right angle as being formed by two line segments that are perpendicular. 
  3. Compare equations of the legs of a right triangle and develop a conjecture about the criteria for perpendicular lines. 
  4. Apply the knowledge of slope criteria to write equations of the lines that are perpendicular to a given line through a point. 
  5. Identify equations of perpendicular lines without graphing. 

Tips for Teachers

  • In this lesson, we are preparing for 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.
  • Students may need to review slope and writing equations of lines before they can fully access this lesson. It is recommended to spend time outside of class building this specific skill.
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Anchor Problems

25-30 minutes

Problem 1

Is the triangle below a right triangle? Explain your reasoning.

Guiding Questions

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Problem 2

Without graphing, determine whether the two sets of equations are perpendicular. Explain your reasoning. 

a.  $${y=3x;\space x+3y=4}$$

b.  $${y-1=-3(x+2);\space12x+4y=32}$$

Guiding Questions

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Problem 3

Write three equations that are perpendicular 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 perpendicular 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 perpendicular to a given line and pass through a given point. 
  • Include problems such as “Is the triangle $${PQR}$$, where $${P(-7,3)}$$, $${Q(-4,7)}$$, and $${R(1,-3)}$$, a right triangle? If so, which angle is the right angle? Justify your reasoning.”

Next

Describe and apply the slope criteria for parallel lines.

Lesson 5
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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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