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Learning Goal
Part of: Use coordinates to prove simple geometric theorems algebraically — 2 of 4 cluster items
Prove slope criteria for lines
HSG.GPE.B.5
**HSG.GPE.B.5**: 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).
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HSG.GPE.B.5: 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).
What you'll learn
- Prove that two non-vertical lines are parallel if and only if they have equal slopes, using the concept of translation or similar triangles formed by the lines and horizontal/vertical reference segments
- Prove that two non-vertical lines are perpendicular if and only if the product of their slopes is -1 (that is, their slopes are negative reciprocals)
- Find the equation of a line parallel to a given line that passes through a specified point
- Find the equation of a line perpendicular to a given line that passes through a specified point
- Apply slope criteria to solve geometric problems involving parallel and perpendicular lines in the coordinate plane
Prerequisites
Slides
Interactive presentations perfect for visual learners • 2 slide decks
Slide Video
Watch narrated slides play like a video lesson • Narrated slide playback