Triangle inequality theorem worksheet

Q: Are these triangle inequality theorem worksheets free?

Yes. Every triangle inequality 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.

Q: Do the triangle inequality theorem worksheets come with an answer key?

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.

Q: Are these triangle inequality theorem worksheets printable?

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.

Q: What grade are these triangle inequality theorem worksheets for?

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.

Q: Can I get a different version of the same triangle inequality theorem worksheet?

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.

Q: Is this a free alternative to Kuta Software for triangle inequality theorem?

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 triangle inequality 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.

Q: Can I choose how hard the triangle inequality theorem questions are?

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.

Q: What kinds of question are on a triangle inequality theorem worksheet?

You pick from 2: the range for the third side and can these be the sides of a triangle. Tick as many as you want and set how many of each, or let it spread them evenly.

Q: What do students get wrong with triangle inequality theorem?

Giving only the upper limit. A side of 1 with sides 7 and 10 does not close up either, so the difference is just as real a limit as the sum.

Any two sides together have to beat the third, which pins the missing side between the difference and the sum of the other two.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name The Triangle Inequality Date Period Give the range for the third side. Write an inequality for the possible lengths of $x$ . Two sides of a triangle measure $10$ and $11$ . Give the range for the length $x$ of the third side. Find the range of possible values of $x$ . Give the range for the third side. A triangle has sides of length $7$ and $5$ . Write an inequality for the length $x$ of the third side. The lengths of two sides of a triangle are $4$ and $31$ . Between what two lengths must the third side, $x$ , lie? Two sticks 8 and 9 units long are two sides of a triangle. Give the range for the length $x$ of the third stick. Write an inequality for the possible lengths of $x$ . Two sides of a triangle measure $27$ and $35$ . Give the range for the length $x$ of the third side. Give the range for the third side. Find the range of possible values of $x$ . Two sticks 9 and 2 units long are two sides of a triangle. Give the range for the length $x$ of the third stick. A triangle has sides of length $10$ and $2$ . Write an inequality for the length $x$ of the third side. The lengths of two sides of a triangle are $7$ and $19$ . Between what two lengths must the third side, $x$ , lie? Two sticks 23 and 26 units long are two sides of a triangle. Give the range for the length $x$ of the third stick. Give the range for the third side. Two sides of a triangle measure $9$ and $18$ . Give the range for the length $x$ of the third side. Write an inequality for the possible lengths of $x$ . Find the range of possible values of $x$ . The lengths of two sides of a triangle are $5$ and $14$ . Between what two lengths must the third side, $x$ , lie? Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

The Triangle Inequality

Date Period

Give the range for the third side.

Write an inequality for the possible lengths of $x$ .
Two sides of a triangle measure $10$ and $11$ . Give the range for the length $x$ of the third side.
Find the range of possible values of $x$ .
Give the range for the third side.
A triangle has sides of length $7$ and $5$ . Write an inequality for the length $x$ of the third side.
The lengths of two sides of a triangle are $4$ and $31$ . Between what two lengths must the third side, $x$ , lie?
Two sticks 8 and 9 units long are two sides of a triangle. Give the range for the length $x$ of the third stick.
Write an inequality for the possible lengths of $x$ .
Two sides of a triangle measure $27$ and $35$ . Give the range for the length $x$ of the third side.
Give the range for the third side.
Find the range of possible values of $x$ .
Two sticks 9 and 2 units long are two sides of a triangle. Give the range for the length $x$ of the third stick.
A triangle has sides of length $10$ and $2$ . Write an inequality for the length $x$ of the third side.
The lengths of two sides of a triangle are $7$ and $19$ . Between what two lengths must the third side, $x$ , lie?
Two sticks 23 and 26 units long are two sides of a triangle. Give the range for the length $x$ of the third stick.
Give the range for the third side.
Two sides of a triangle measure $9$ and $18$ . Give the range for the length $x$ of the third side.
Write an inequality for the possible lengths of $x$ .
Find the range of possible values of $x$ .
The lengths of two sides of a triangle are $5$ and $14$ . Between what two lengths must the third side, $x$ , lie?



Sigma Prep · sigmaprep.io/worksheets Name The Triangle InequalityAnswer keyVersion 1 Date Period Give the range for the third side. Write an inequality for the possible lengths of $x$ . $4 < x < 8$ Two sides of a triangle measure $10$ and $11$ . Give the range for the length $x$ of the third side. $1 < x < 21$ Find the range of possible values of $x$ . $3 < x < 17$ Give the range for the third side. $6 < x < 16$ A triangle has sides of length $7$ and $5$ . Write an inequality for the length $x$ of the third side. $2 < x < 12$ The lengths of two sides of a triangle are $4$ and $31$ . Between what two lengths must the third side, $x$ , lie? $27 < x < 35$ Two sticks 8 and 9 units long are two sides of a triangle. Give the range for the length $x$ of the third stick. $1 < x < 17$ Write an inequality for the possible lengths of $x$ . $8 < x < 18$ Two sides of a triangle measure $27$ and $35$ . Give the range for the length $x$ of the third side. $8 < x < 62$ Give the range for the third side. $6 < x < 14$ Find the range of possible values of $x$ . $3 < x < 19$ Two sticks 9 and 2 units long are two sides of a triangle. Give the range for the length $x$ of the third stick. $7 < x < 11$ A triangle has sides of length $10$ and $2$ . Write an inequality for the length $x$ of the third side. $8 < x < 12$ The lengths of two sides of a triangle are $7$ and $19$ . Between what two lengths must the third side, $x$ , lie? $12 < x < 26$ Two sticks 23 and 26 units long are two sides of a triangle. Give the range for the length $x$ of the third stick. $3 < x < 49$ Give the range for the third side. $1 < x < 7$ Two sides of a triangle measure $9$ and $18$ . Give the range for the length $x$ of the third side. $9 < x < 27$ Write an inequality for the possible lengths of $x$ . $4 < x < 64$ Find the range of possible values of $x$ . $5 < x < 11$ The lengths of two sides of a triangle are $5$ and $14$ . Between what two lengths must the third side, $x$ , lie? $9 < x < 19$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

The Triangle InequalityAnswer keyVersion 1

Date Period

Give the range for the third side.

Write an inequality for the possible lengths of $x$ . $4 < x < 8$
Two sides of a triangle measure $10$ and $11$ . Give the range for the length $x$ of the third side. $1 < x < 21$
Find the range of possible values of $x$ . $3 < x < 17$
Give the range for the third side. $6 < x < 16$
A triangle has sides of length $7$ and $5$ . Write an inequality for the length $x$ of the third side. $2 < x < 12$
The lengths of two sides of a triangle are $4$ and $31$ . Between what two lengths must the third side, $x$ , lie? $27 < x < 35$
Two sticks 8 and 9 units long are two sides of a triangle. Give the range for the length $x$ of the third stick. $1 < x < 17$
Write an inequality for the possible lengths of $x$ . $8 < x < 18$
Two sides of a triangle measure $27$ and $35$ . Give the range for the length $x$ of the third side. $8 < x < 62$
Give the range for the third side. $6 < x < 14$
Find the range of possible values of $x$ . $3 < x < 19$
Two sticks 9 and 2 units long are two sides of a triangle. Give the range for the length $x$ of the third stick. $7 < x < 11$
A triangle has sides of length $10$ and $2$ . Write an inequality for the length $x$ of the third side. $8 < x < 12$
The lengths of two sides of a triangle are $7$ and $19$ . Between what two lengths must the third side, $x$ , lie? $12 < x < 26$
Two sticks 23 and 26 units long are two sides of a triangle. Give the range for the length $x$ of the third stick. $3 < x < 49$
Give the range for the third side. $1 < x < 7$
Two sides of a triangle measure $9$ and $18$ . Give the range for the length $x$ of the third side. $9 < x < 27$
Write an inequality for the possible lengths of $x$ . $4 < x < 64$
Find the range of possible values of $x$ . $5 < x < 11$
The lengths of two sides of a triangle are $5$ and $14$ . Between what two lengths must the third side, $x$ , lie? $9 < x < 19$

How to do these

Two sides of a triangle are $7$ and $10$ . Give the range for the third side

It must be less than 7 plus 10.
And more than 10 minus 7.

The answer is $3 < x < 17$ .

Where students go wrong

Giving only the upper limit. A side of 1 with sides 7 and 10 does not close up either, so the difference is just as real a limit as the sum.

Also called possible side lengths or third side of a triangle.

What you can put on this worksheet

The range for the third side: Find the range of possible values of $x$ . — a triangle with two sides 8 and 10 → $2 < x < 18$
Can these be the sides of a triangle: Is there a triangle with sides $8$ , $16$ and $7$ ? → No

Questions about these worksheets