Prove slope criteria for lines

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Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework

Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
Guided Notes →One page your students fill in and keep.
Exit Ticket →Three items at the end of class. No student accounts.
Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
Homework →Assign practice; it grades itself.

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).

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

Review first: