CCSS.Math.Content.HSG-GPE.B.5
The standard
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).
Common Core State Standards for Mathematics
What this standard means
Students need to explain why parallel lines have the same slope and why perpendicular lines have slopes that multiply to -1. They also need to use those facts to write equations of lines through a point, check relationships between lines, and solve coordinate geometry problems.
Mastery looks like moving between a graph, two points, a slope, and an equation without guessing. Students can justify their steps, not just say “same slope” or “opposite reciprocal.” Common trouble spots are vertical and horizontal lines, sign errors with perpendicular slopes, and mixing up slope with y-intercept.
Ways to teach it
- Give pairs graph paper, rulers, and four point pairs, then have them draw lines, calculate slopes, and sort parallel, perpendicular, or neither.
- Ask students to explain why a line with slope 3 cannot be perpendicular to a line with slope 1/3.
- Exit ticket: Find the equation of a line through (2, -5) perpendicular to y = -4x + 7, then justify the slope.
- Use a city street map grid and ask students to write equations for a new road parallel to one street and perpendicular to another.
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Related standards
- CCSS.Math.Content.8.EE.B.6
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation...
- CCSS.Math.Content.HSG-CO.C.9
Prove theorems about lines and angles.
- CCSS.Math.Content.HSG-CO.C
Prove geometric theorems
- CCSS.Math.Content.HSG-SRT.B.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.