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Constructing triangles worksheet

Grade 7 math, Common Core 7.G.A.2. 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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Constructing triangles

Grade 7 math, Common Core 7.G.A.2

Answer each question about building triangles.

  1. 1.
    Can 9 cm, 5 cm and 6 cm be the sides of a triangle?
  2. 2.
    Can 2 cm, 10 cm and 7 cm be the sides of a triangle?
  3. 3.
    Can a triangle have angles of 98°, 40° and 32°?
  4. 4.
    Two sides of a triangle are 11 in and 8 in. What lengths can the third side be?
  5. 5.
    Two sides of a triangle are 3 in and 12 in. What lengths can the third side be?
  6. 6.
    Can 9 cm, 12 cm and 15 cm be the sides of a triangle?
  7. 7.
    Two sides of a triangle are 12 in and 4 in. What lengths can the third side be?
  8. 8.
    Two sides of a triangle are 6 in and 12 in. What lengths can the third side be?
  9. 9.
    Can 3 cm, 6 cm and 3 cm be the sides of a triangle?
  10. 10.
    Can a triangle have angles of 26°, 103° and 51°?
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Constructing triangles

Grade 7 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. Yes. 5 + 6 = 11, which is more than 9.

  2. 2. No. 2 + 7 = 9, which is not more than 10.

  3. 3. No. They add up to 170°, not 180°.

  4. 4. More than 3 in and less than 19 in

    11 − 8 = 311 + 8 = 19

  5. 5. More than 9 in and less than 15 in

    12 − 3 = 93 + 12 = 15

  6. 6. Yes. 9 + 12 = 21, which is more than 15.

  7. 7. More than 8 in and less than 16 in

    12 − 4 = 812 + 4 = 16

  8. 8. More than 6 in and less than 18 in

    12 − 6 = 66 + 12 = 18

  9. 9. No. 3 + 3 = 6, which is not more than 6.

  10. 10. Yes. They add up to 180°.

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

About constructing triangles

Not every three lengths make a triangle. The triangle inequality says the two shorter sides must add up to more than the longest side, or they can’t meet. The three angles of a triangle always add up to 180°, so three angles that don’t add to 180° can’t form one.

Worked example 1

Two sides of a triangle are 5 in and 6 in. What lengths can the third side be?
  1. Step 1.6 − 5 = 1
  2. Step 2.5 + 6 = 11

Answer: More than 1 in and less than 11 in

Example 2

Can 8 cm, 8 cm and 3 cm be the sides of a triangle?

Answer: Yes. 3 + 8 = 11, which is more than 8.

Example 3

Can a triangle have angles of 40°, 67° and 73°?

Answer: Yes. They add up to 180°.

Watch out for

  • Add the two shorter sides and compare with the longest side.
  • If the two shorter sides add up to exactly the longest side, they lie flat: no triangle.
  • For the third side, it must be longer than the difference and shorter than the sum of the other two.

Practice constructing triangles online

On StudyWiz, your kid can practice constructing triangles 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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