Georgia 7.PAR.4.7
The Standard
Use similar triangles to explain why the slope, m, is the same between any two distinct points on a nonvertical line in the coordinate plane.
Georgia's K-12 Mathematics Standards · Recognize proportional relationships in relevant, mathematical problems; represent, solve, and explain these relationships with tables, graphs, and equations.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students draw right triangles between pairs of points on a nonvertical line and compare each triangle’s rise and run. They show the triangles are similar, then use corresponding sides to explain why the slope stays constant.
What Mastery Looks Like
- Students can draw slope triangles using different pairs of points on one line and calculate equal rise-to-run ratios. They explain that the triangles have equal angles, so corresponding side lengths are proportional.
Common Misconceptions
- Students may divide run by rise or lose the sign when the line slopes downward. They may compare noncorresponding sides or claim the slopes match without explaining why the right triangles are similar.
How to Assess It
- Exit ticket: Plot A(1, 2), B(3, 5), and C(7, 11), then draw slope triangles for AB and BC. Show that the triangles are similar and use corresponding side ratios to explain why both segments have the same slope.
Lesson moves
Ways to Teach It
On graph paper, students choose three points on one line, draw two slope triangles, measure the legs, and compare each rise-to-run ratio.
Write an explanation: Why do two different slope triangles on the same nonvertical line produce equal rise-to-run ratios?
Play Slope Triangle Match: pair cards showing triangles from the same line, then justify each match using corresponding side ratios.
Use a scale drawing of a ramp to compare rise over run for two sections and explain why the steepness stays constant.
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