Virginia SOL Math / Grade 7 / Measurement & Geometry

7.MG.2

Similarity & Proportional Reasoning

What you'll learn

  • Identify similar figures and their corresponding parts
  • Use proportions to find unknown side lengths in similar figures
  • Apply a scale factor between similar figures

Words to know

Similar figures —
figures with the same shape but not always the same size
Corresponding sides —
sides in the same position in two similar figures
Scale factor —
the number that multiplies one figure to get a similar one
Proportion —
an equation stating that two ratios are equal
Congruent —
having exactly the same size and shape

Why it matters Similar figures let us find real distances from a map, a model, or a shadow without measuring them directly.

Worked examples

Model ItI do

Two similar rectangles have corresponding sides 4 and 12. What is the scale factor from the small to the large?

Divide a large side by its matching small side: 12 divided by 4 = 3. The scale factor from small to large is 3.

Try It TogetherWe do

Two triangles are similar. A side of 6 matches a side of 9. If another side of the first is 8, find the matching side of the second.

Set up a proportion: 6 over 9 equals 8 over x. Cross multiply: 6x = 72, so x = 12. The matching side is 12.

Now YouYou do

Two similar figures have a scale factor of 2. A side on the small figure is 7. Find the matching side on the large figure.

Multiply the small side by the scale factor. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Find the scale factor when a side of 3 becomes 12.

  2. 2.Solve: 2 over 3 equals x over 9.

  3. 3.Two similar figures have a scale factor of 3. A side of 5 corresponds to what length?

On Level

The core Quick Check from the book.

  1. 1.Find the scale factor when a side of 5 becomes 15.

  2. 2.Solve: 3 over 4 equals x over 8.

  3. 3.Two similar rectangles: sides 2 and 10 correspond. What is the scale factor?

  4. 4.A model uses 1 cm for 4 m. How many meters does 6 cm represent?

  5. 5.Similar triangles: 4 matches 6, and 10 matches x. Find x.

Challenge

Stretch your thinking.

  1. 1.Two triangles are similar. A side of 8 matches a side of 20. If another side of the first triangle is 6, find the matching side of the second.

  2. 2.A 6 foot tall person casts a 4 foot shadow. A nearby tree casts a 30 foot shadow at the same time. How tall is the tree?

  3. 3.On a map, 1 cm represents 8 km. Two towns are 7.5 cm apart on the map. What is the actual distance?