Virginia SOL 7.MG.2.e
The Standard
Recognize and justify if two quadrilaterals or triangles are similar using the ratios of corresponding side lengths.
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 figures and calculate each side-length ratio in a consistent order. They decide whether one scale factor applies throughout and show calculations that support the decision.
What Mastery Looks Like
- Students correctly match corresponding sides, even when a figure is rotated or reflected. They simplify each ratio consistently, identify the scale factor, and use equal or unequal ratios to support their conclusion.
Common Misconceptions
- Students may compare sides in the wrong order or reverse only one ratio. They may check one pair of sides and stop, or trust figures that look alike without calculating every ratio.
How to Assess It
- Give △ABC with sides 6, 9, 12 and △DEF with sides 10, 15, 20. Ask students to decide whether they are similar and support the answer with three ratios.
Lesson moves
Ways to Teach It
Give students straws cut to labeled lengths, then have them build, match, and compare pairs of triangles using side ratios.
Ask students to write a response to: Why is checking only one pair of corresponding sides not enough?
Run a card sort where students match figure pairs with ratio calculations, then label each pair similar or not similar.
Compare the length and width of printed photos in two sizes to decide whether one is a true enlargement of the other.
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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.2.a
Identify corresponding congruent angles of similar quadrilaterals and triangles, through the use of geometric markings.
- 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.
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