Worksheets · Geometry

Inequalities in one triangle worksheet

Sides and angles run in the same order: the biggest angle is opposite the longest side, every time. So ordering one orders the other, and the whole question is reading which side faces which angle.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Inequalities in One Triangle

Date Period

Order the sides or angles as asked.

  1. A triangle has angles A=56∘, B=15∘, C=109∘. List the sides shortest first
  2. A triangle has a=21, b=18, c=23. List the angles smallest first
  3. A triangle has a=14, b=13, c=16. List the angles smallest first
  4. A triangle has angles A=19∘, B=41∘, C=120∘. List the sides shortest first
  5. A triangle has a=17, b=19, c=14. List the angles smallest first
  6. A triangle has angles A=28∘, B=58∘, C=94∘. List the sides shortest first
  7. A triangle has angles A=65∘, B=27∘, C=88∘. List the sides shortest first
  8. A triangle has angles A=44∘, B=65∘, C=71∘. List the sides shortest first
  9. A triangle has a=13, b=12, c=11. List the angles smallest first
  10. A triangle has a=9, b=14, c=16. List the angles smallest first
  11. A triangle has angles A=30∘, B=80∘, C=70∘. List the sides shortest first
  12. A triangle has angles A=41∘, B=34∘, C=105∘. List the sides shortest first
  13. A triangle has angles A=77∘, B=75∘, C=28∘. List the sides shortest first
  14. A triangle has angles A=75∘, B=70∘, C=35∘. List the sides shortest first
  15. A triangle has angles A=22∘, B=17∘, C=141∘. List the sides shortest first
  16. A triangle has angles A=48∘, B=76∘, C=56∘. List the sides shortest first
  17. A triangle has angles A=25∘, B=59∘, C=96∘. List the sides shortest first
  18. A triangle has a=12, b=14, c=13. List the angles smallest first
  19. A triangle has angles A=58∘, B=48∘, C=74∘. List the sides shortest first
  20. A triangle has angles A=20∘, B=68∘, C=92∘. List the sides shortest first

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

Sigma Prep · sigmaprep.io/worksheets

Name

Inequalities in One TriangleAnswer keyVersion 1

Date Period

Order the sides or angles as asked.

  1. A triangle has angles A=56∘, B=15∘, C=109∘. List the sides shortest firstb, a, c
  2. A triangle has a=21, b=18, c=23. List the angles smallest firstB, A, C
  3. A triangle has a=14, b=13, c=16. List the angles smallest firstB, A, C
  4. A triangle has angles A=19∘, B=41∘, C=120∘. List the sides shortest firsta, b, c
  5. A triangle has a=17, b=19, c=14. List the angles smallest firstC, A, B
  6. A triangle has angles A=28∘, B=58∘, C=94∘. List the sides shortest firsta, b, c
  7. A triangle has angles A=65∘, B=27∘, C=88∘. List the sides shortest firstb, a, c
  8. A triangle has angles A=44∘, B=65∘, C=71∘. List the sides shortest firsta, b, c
  9. A triangle has a=13, b=12, c=11. List the angles smallest firstC, B, A
  10. A triangle has a=9, b=14, c=16. List the angles smallest firstA, B, C
  11. A triangle has angles A=30∘, B=80∘, C=70∘. List the sides shortest firsta, c, b
  12. A triangle has angles A=41∘, B=34∘, C=105∘. List the sides shortest firstb, a, c
  13. A triangle has angles A=77∘, B=75∘, C=28∘. List the sides shortest firstc, b, a
  14. A triangle has angles A=75∘, B=70∘, C=35∘. List the sides shortest firstc, b, a
  15. A triangle has angles A=22∘, B=17∘, C=141∘. List the sides shortest firstb, a, c
  16. A triangle has angles A=48∘, B=76∘, C=56∘. List the sides shortest firsta, c, b
  17. A triangle has angles A=25∘, B=59∘, C=96∘. List the sides shortest firsta, b, c
  18. A triangle has a=12, b=14, c=13. List the angles smallest firstA, C, B
  19. A triangle has angles A=58∘, B=48∘, C=74∘. List the sides shortest firstb, a, c
  20. A triangle has angles A=20∘, B=68∘, C=92∘. List the sides shortest firsta, b, c

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

How to do these

A=40∘, B=60∘, C=80∘

  1. Side a faces angle A, and so on.
  2. The angles go 40, 60, 80.
  3. So the sides go in the same order.

The answer is a, b, c.

Where students go wrong

Matching a side to the angle next to it. Each side is named for the angle across from it, not the ones it touches, and getting that backwards reverses the whole list.

Also called ordering sides and angles, largest angle largest side or triangle inequalities.

Questions about these worksheets

Yes. Every inequalities in one triangle 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 inequalities in one triangle 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.

Matching a side to the angle next to it. Each side is named for the angle across from it, not the ones it touches, and getting that backwards reverses the whole list.