Worksheets · Geometry

Converse of the Pythagorean theorem worksheet

Square the two shorter sides and add. If the total equals the square of the longest side, the triangle is right. If it is more, the triangle is acute; if it is less, obtuse. The longest side always goes on its own.

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Name

Converse of the Pythagorean Theorem

Date Period

Classify each triangle from its sides.

  1. A triangle has sides 28,21,20. Right, acute or obtuse?
  2. A triangle has sides 10,24,27. Right, acute or obtuse?
  3. A triangle has sides 7,24,24. Right, acute or obtuse?
  4. A triangle has sides 24,7,24. Right, acute or obtuse?
  5. A triangle has sides 8,6,9. Right, acute or obtuse?
  6. A triangle has sides 40,42,59. Right, acute or obtuse?
  7. A triangle has sides 120,27,123. Right, acute or obtuse?
  8. A triangle has sides 17,15,8. Right, acute or obtuse?
  9. A triangle has sides 5,4,3. Right, acute or obtuse?
  10. A triangle has sides 15,36,40. Right, acute or obtuse?
  11. A triangle has sides 88,63,60. Right, acute or obtuse?
  12. A triangle has sides 27,120,123. Right, acute or obtuse?
  13. A triangle has sides 21,16,12. Right, acute or obtuse?
  14. A triangle has sides 9,12,15. Right, acute or obtuse?
  15. A triangle has sides 16,15,8. Right, acute or obtuse?
  16. A triangle has sides 9,12,16. Right, acute or obtuse?
  17. A triangle has sides 24,51,45. Right, acute or obtuse?
  18. A triangle has sides 3,5,4. Right, acute or obtuse?
  19. A triangle has sides 50,48,14. Right, acute or obtuse?
  20. A triangle has sides 6,8,10. Right, acute or obtuse?

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Converse of the Pythagorean TheoremAnswer keyVersion 1

Date Period

Classify each triangle from its sides.

  1. A triangle has sides 28,21,20. Right, acute or obtuse?Acute
  2. A triangle has sides 10,24,27. Right, acute or obtuse?Obtuse
  3. A triangle has sides 7,24,24. Right, acute or obtuse?Acute
  4. A triangle has sides 24,7,24. Right, acute or obtuse?Acute
  5. A triangle has sides 8,6,9. Right, acute or obtuse?Acute
  6. A triangle has sides 40,42,59. Right, acute or obtuse?Obtuse
  7. A triangle has sides 120,27,123. Right, acute or obtuse?Right
  8. A triangle has sides 17,15,8. Right, acute or obtuse?Right
  9. A triangle has sides 5,4,3. Right, acute or obtuse?Right
  10. A triangle has sides 15,36,40. Right, acute or obtuse?Obtuse
  11. A triangle has sides 88,63,60. Right, acute or obtuse?Obtuse
  12. A triangle has sides 27,120,123. Right, acute or obtuse?Right
  13. A triangle has sides 21,16,12. Right, acute or obtuse?Obtuse
  14. A triangle has sides 9,12,15. Right, acute or obtuse?Right
  15. A triangle has sides 16,15,8. Right, acute or obtuse?Acute
  16. A triangle has sides 9,12,16. Right, acute or obtuse?Obtuse
  17. A triangle has sides 24,51,45. Right, acute or obtuse?Right
  18. A triangle has sides 3,5,4. Right, acute or obtuse?Right
  19. A triangle has sides 50,48,14. Right, acute or obtuse?Right
  20. A triangle has sides 6,8,10. Right, acute or obtuse?Right

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

A triangle has sides 7,24,25. Right, acute or obtuse?

  1. 7² + 24² = 49 + 576 = 625.
  2. 25² = 625. They match.

The answer is Right.

Where students go wrong

Squaring the wrong side on its own. The comparison only works with the longest side alone on one side of the equation.

Also called classifying triangles by sides, Pythagorean inequalities, is it a right triangle or Pythagorean triples.

Questions about these worksheets

Yes. Every converse of the pythagorean theorem sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the converse of the pythagorean theorem questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Squaring the wrong side on its own. The comparison only works with the longest side alone on one side of the equation.