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).

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
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes


Geometry - Fluency Recommendations

Fluency with the use of coordinates to establish geometric results, calculate length and angle, and use geometric representations as a modeling tool are some of the most valuable tools in mathematics and related fields.


  • Item Type(s): This benchmark may be assessed using: EE item(s)

  • Assessment Limits :
    Lines may include horizontal and vertical lines.

    Items may not ask the student to provide only the slope of a parallel
    or perpendicular line.

  • Calculator :


  • Clarification :
    Students will prove the slope criteria for parallel lines.

    Students will prove the slope criteria for perpendicular lines.

    Students will find equations of lines using the slope criteria for
    parallel and perpendicular lines.

  • Stimulus Attributes :
    Items may be set in a real-world or mathematical context.
  • Response Attributes :
    Items may require the student to be familiar with slope-intercept
    form of a line, standard form of a line, and point-slope form of a line.


  • Test Item #: Sample Item 1
  • Question:

    The equation for line A is shown.

    y=begin mathsize 12px style negative 2 over 3 x minus 4 end style

    Line A and line B are perpendicular, and the point (-2,1_ lies on line B.

    Write an equation for line B.

  • Difficulty: N/A
  • Type: EE: Equation Editor