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Grade 10 triangle inequality worksheets

HSG-CO.C.10 Measurement and geometry

Printable triangle inequality worksheets for grade 10, aligned to Common Core standard HSG-CO.C.10. Can these sides make a triangle?.

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Sample problems

  1. Two sides of a triangle are 11 and 12. The third side must be between which two values? 1 and 23
  2. Can sides of 10, 10 and 25 form a triangle? no
  3. Two sides of a triangle are 6 and 13. The third side must be between which two values? 7 and 19
  4. Two sides of a triangle are 10 and 11. The third side must be between which two values? 1 and 21
  5. Can sides of 12, 12 and 27 form a triangle? no
  6. Two sides of a triangle are 7 and 10. The third side must be between which two values? 3 and 17
  7. Can sides of 7, 13 and 22 form a triangle? no
  8. Can sides of 7, 14 and 26 form a triangle? no

These eight are one sample at medium difficulty — the generator makes a different set every time.

A worked example

Two sides of a triangle are 11 and 12. The third side must be between which two values? 1 and 23

  1. Any side must be less than the sum of the other two: less than 11 + 12 = 23
  2. And more than their difference: more than 12 − 11 = 1
  3. So the third side is between 1 and 23

Every problem on the answer key can show its steps like this — turn on “Show steps” before downloading.

About these worksheets

Each problem states its own measurements, so the reasoning is the same but the arithmetic is new every time. Every sheet is generated fresh, so you can print a new one on the same skill as often as you need — different numbers, same difficulty.

Pick how many problems you want and whether they should be easy, medium or hard, then download a PDF with a matching answer key. The key can show the worked steps for every problem, which is what a parent needs to see where a wrong answer went wrong.

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