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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).

Standard #: MAFS.912.G-GPE.2.5Archived Standard
Standard Information
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Expressing Geometric Properties with Equations
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Use coordinates to prove simple geometric theorems algebraically. (Geometry - Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Related Courses
Related Resources
Formative Assessments
Lesson Plans
  • Graphing Equations on the Cartesian Plane: Slope The lesson teaches students about an important characteristic of lines: their slope. Slope can be determined either in graphical or algebraic form. Slope can also be described as positive, negative, zero, or undefined. Students get an explanation of when and how these different types of slopes occur. Finally, students learn how slope relates to parallel and perpendicular lines. When two lines are parallel, they have the same slope and when they are perpendicular their slopes are negative reciprocals of one another. Prerequisite knowledge: Students must know how to graph points on the Cartesian plane. They must be familiar with the x- and y-axis on the plane in both the positive and negative directions.
  • Finding Equations of Parallel and Perpendicular Lines This lesson assesses how well students understand the relationship between the slopes of parallel and perpendicular lines. A sorting activity is included where students group equations that represent lines with the same slope, y-intercept, parallel or perpendicular, etc. The lesson also aims to encourage discussion on common misconceptions about equations of lines.
  • When Will We Ever Meet? Students will be guided through the investigation of y = mx+b. Through this lesson, students will be able to determine whether lines are parallel, perpendicular, or neither by looking at the graph and the equation.
  • Investigating Lines With Our Minds! Discover the relationships between the slopes of parallel and perpendicular lines. Students write the equations of lines parallel and/or perpendicular to a given line through a given point. Directions for using graph paper or x-y coordinate pegboards are given.
Problem-Solving Tasks
  • A Midpoint Miracle This problem solving task gives students the opportunity to prove a fact about quadrilaterals: that if we join the midpoints of an arbitrary quadrilateral to form a new quadrilateral, then the new quadrilateral is a parallelogram, even if the original quadrilateral was not.
  • Unit Squares and Triangles This problem solving task asks students to find the area of a triangle by using unit squares and line segments.
  • Triangles inscribed in a circle This problem solving task challenges students to use ideas about linear functions in order to determine when certain angles are right angles.
Teaching Idea
  • Midpoints of the Sides of a Quadrilateral The students will construct a quadrilateral on graph paper, determine the midpoints of each of the four sides, then connect the midpoints of adjacent sides. The question then is the following: what are the properties of the resulting quadrilateral? Students need to justify their conclusions.
Video/Audio/Animations
  • Parallel Lines 2 This video shows how to determine which lines are parallel from a set of three different equations.
  • Parallel Lines This video illustrates how to determine if the graphs of a given set of equations are parallel.
  • Perpendicular Lines 2 This video describes how to determine the equation of a line that is perpendicular to another line. All that is given initially the equation of a line and an ordered pair from the other line.
MFAS Formative Assessments
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