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Congruence and similarity worksheet

Grade 8 math, Common Core 8.G.A.4. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

By the StudyWiz teamUpdated October 23, 2026How we write our pages

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Congruence and similarity

Grade 8 math, Common Core 8.G.A.4

Answer each question about congruent and similar figures.

  1. 1.
    Is a 6 cm by 7 cm rectangle similar to a 18 cm by 21 cm rectangle?
  2. 2.
    Triangle ABC is similar to triangle DEF. AB = 10, BC = 6 and DE = 20. Find EF.
  3. 3.
    Triangle ABC is similar to triangle DEF. AB = 10, BC = 12 and DE = 25. Find EF.
  4. 4.
    Is a 2 cm by 7 cm rectangle similar to a 4 cm by 14 cm rectangle?
  5. 5.
    Triangle ABC is similar to triangle DEF. AB = 8, BC = 14 and DE = 12. Find EF.
  6. 6.
    A 6-foot pole casts a 2-foot shadow. At the same time, a tree casts a 10-foot shadow. How tall is the tree?
  7. 7.
    Triangle ABC is similar to triangle DEF. AB = 8, BC = 8 and DE = 16. Find EF.
  8. 8.
    Is a 3 cm by 8 cm rectangle similar to a 4.5 cm by 13 cm rectangle?
  9. 9.
    A shape is dilated by a scale factor of 5. How many times bigger are its side lengths? Its area?
  10. 10.
    Is a 5 cm by 8 cm rectangle similar to a 7.5 cm by 12 cm rectangle?
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Congruence and similarity

Grade 8 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. Yes. Both sides grow by 3.

  2. 2. EF = 12

    Scale factor: 20 ÷ 10 = 26 × 2 = 12

  3. 3. EF = 30

    Scale factor: 25 ÷ 10 = 2.512 × 2.5 = 30

  4. 4. Yes. Both sides grow by 2.

  5. 5. EF = 21

    Scale factor: 12 ÷ 8 = 1.514 × 1.5 = 21

  6. 6. 30 feet

    The triangles are similar: 62 = t10t = 6 × 5 = 30

  7. 7. EF = 16

    Scale factor: 16 ÷ 8 = 28 × 2 = 16

  8. 8. No. 4.5 ÷ 3 = 1.5, but 13 ÷ 8 = 1.63.

  9. 9. Sides 5 times; area 25 times

    Area grows by 5² = 25

  10. 10. Yes. Both sides grow by 1.5.

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About congruence and similarity

Congruent figures have the same size and shape: one can be moved onto the other by translations, reflections and rotations. Similar figures have the same shape but maybe a different size: one is a dilation of the other. In similar figures, matching angles are equal and matching sides are in proportion, with the same scale factor.

Worked example 1

Triangle ABC is similar to triangle DEF. AB = 10, BC = 4 and DE = 25. Find EF.
  1. Step 1.Scale factor: 25 ÷ 10 = 2.5
  2. Step 2.4 × 2.5 = 10

Answer: EF = 10

Worked example 2

A shape is dilated by a scale factor of 4. How many times bigger are its side lengths? Its area?
  1. Step 1.Area grows by 4² = 16

Answer: Sides 4 times; area 16 times

Worked example 3

A 6-foot pole casts a 8-foot shadow. At the same time, a tree casts a 56-foot shadow. How tall is the tree?
  1. Step 1.The triangles are similar: 68 = t56
  2. Step 2.t = 6 × 7 = 42

Answer: 42 feet

Watch out for

  • Match the sides in the same order as the letters: AB matches DE.
  • Scale factor = new length ÷ original length.
  • If the scale factor is k, areas grow by k² (not k).

Practice congruence and similarity online

On StudyWiz, your kid can practice congruence and similarity with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

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