Virginia SOL 7.MG.2.d
The Standard
Write proportions to express the relationships between the lengths of corresponding sides of similar quadrilaterals and triangles.
Virginia Standards of Learning for Mathematics · The student will solve problems and justify relationships of similarity using proportional reasoning.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students match sides in pairs of similar triangles and quadrilaterals. They set ratios of matching side lengths equal, keep the figure order consistent, and explain the shared scale factor.
What Mastery Looks Like
- Given two figures with different orientations, students correctly pair every corresponding side and write several valid proportions. They can verify each proportion by cross multiplication or by finding the common scale factor.
Common Misconceptions
- Students often pair sides by position on the page instead of matching vertices or angle relationships. They may reverse only one ratio, mix side order, or assume figures are similar because they look alike.
How to Assess It
- Exit ticket: Triangles ABC and DEF are similar, with A matching D, B matching E, and C matching F. Write two valid proportions using their side names, then explain how you kept the side order consistent.
Lesson moves
Ways to Teach It
Give pairs of similar paper triangles; students color corresponding sides alike, measure them, and arrange side-length cards into a true proportion.
Display two rotated quadrilaterals and ask, "Which sides correspond, and how does vertex order prove it?" Students write and compare explanations.
Play Proportion Match: teams pair figure cards with proportion cards, earning a point only when they justify the matching side order.
Use dimensions from two similar phone-screen images; students write a proportion to check whether one image is a true scaled copy.
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Related Standards
- 7.MG.2.f
Solve a proportion to determine a missing side length of similar quadrilaterals or triangles.
- 7.MG.2.c
Given two similar quadrilaterals or triangles, write similarity statements using symbols.
- 7.MG.2.b
Identify corresponding sides of similar quadrilaterals and triangles.
- 7.MG.2.e
Recognize and justify if two quadrilaterals or triangles are similar using the ratios of corresponding side lengths.
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