Virginia SOL 7.MG.2.f
The Standard
Solve a proportion to determine a missing side length of similar quadrilaterals or 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 corresponding sides in two similar figures. They write equivalent ratios in a consistent order and use multiplication or division to find an unknown length. They check that the answer fits the scale factor.
What Mastery Looks Like
- Given two labeled triangles or quadrilaterals, a student identifies corresponding sides even when the figures have different orientations. The student solves accurately and explains why the resulting length is reasonable.
Common Misconceptions
- Students may pair sides by position on the page instead of matching vertices or angle markings. They may reverse one ratio, use an additive difference, or apply the scale factor in the wrong direction.
How to Assess It
- Exit ticket: Triangle ABC is similar to triangle DEF, with AB = 6, DE = 9, and BC = 10. Find EF and show the proportion you used.
Lesson moves
Ways to Teach It
Give pairs of scaled cardstock triangles; students measure corresponding sides, calculate each ratio, and use the common scale factor to predict one covered length.
Display two rotated similar quadrilaterals and ask, "Which sides correspond, and how do you know before calculating?"
Play Ratio Match: students pair figure cards with proportion cards, then solve the unknown length to keep each matched set.
Use a floor plan scale to calculate the actual length of a wall from its matching drawing measurement.
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Related Standards
- 7.MG.2.d
Write proportions to express the relationships between the lengths of corresponding sides of similar quadrilaterals and triangles.
- 7.MG.3.d
Given a diagram, determine an unknown side length in a quadrilateral using properties of quadrilaterals.
- 7.MG.2.g
Given angle measures in a quadrilateral or triangle, determine unknown angle measures in a similar quadrilateral or triangle.
- 7.MG.2.b
Identify corresponding sides of similar quadrilaterals and triangles.
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