Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Slopes of parallel and perpendicular lines
Prove parallel and perpendicular slope criteria and construct corresponding lines
Problem types
- Parallel and perpendicular slopes
- Point-slope equation of a parallel or perpendicular line
- Classify two lines as parallel, perpendicular, the same or neither
- Complete a slope proof
- Parallel line through an intercept
Builds on
- Proofs that use coordinates
- Theorems about similar triangles · Useful idea
Similar right triangles on two perpendicular lines show their slopes are negative reciprocals.
Leads to
- A tangent from a point outside a circle · See it applied
A tangent is perpendicular to the radius at the point of tangency, and perpendicular lines have slopes whose product is -1.
- Linear equations from constraints · See it applied
Parallel and perpendicular lines have equations with equal or negative reciprocal slopes, used to write the equation of a line.
Related skills
- Vectors and their components · Related idea
Two lines are perpendicular exactly when their direction vectors have dot product zero, which is the same as slopes whose product is -1.
Open the interactive map to explore lessons and skill connections.