MA19.GDA.33

Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.33

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

Unpacked Content

Knowledge

Students know:
  • Techniques to find the slope of a line.
  • Key features needed to solve geometric problems.
  • Techniques for presenting a proof of geometric theorems.

Skills

Students are able to:
  • Explain and justify conclusions reached regarding the slopes of parallel and perpendicular lines.
  • Apply slope criteria for parallel and perpendicular lines to accurately find the solutions of geometric problems and justify the solutions.
  • Communicate logical reasoning in a systematic way to present a mathematical proof of geometric theorems.

Understanding

Students understand that:
  • Relationships exist between the slope of a line and any line parallel or perpendicular to that line.
  • Slope criteria for parallel and perpendicular lines may be useful in solving geometric problems.

Vocabulary

  • Parallel lines
  • Perpendicular lines
  • Slope
  • Slope triangle

COS Examples

Example: Find the equation of a line parallel or perpendicular to a given line that passes through a given point.

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