Inequalities in one triangle worksheet

Q: Are these inequalities in one triangle worksheets free?

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.

Q: Do the inequalities in one triangle 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 inequalities in one triangle 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 inequalities in one triangle 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 inequalities in one triangle 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 inequalities in one triangle?

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.

Q: Can I choose how hard the inequalities in one triangle 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 inequalities in one triangle worksheet?

You pick from 4: ordering sides and angles, name the largest or smallest, the range an angle can take and ordering, read off a drawing. Tick as many as you want and set how many of each, or let it spread them evenly.

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.

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



Sigma Prep · sigmaprep.io/worksheets Name Inequalities in One Triangle Date Period Order or name the sides or angles as asked. Order the sides or angles In a triangle, $m ∠ A = 51^{\circ}$ , $m ∠ B = 20^{\circ}$ and $m ∠ C = 109^{\circ}$ . List the sides shortest first. A triangle has $a = 8$ , $b = 10$ , $c = 11$ . List the angles smallest first. A triangle has $a = 22$ , $b = 27$ , $c = 23$ . List the angles smallest first. In a triangle, $m ∠ A = 54^{\circ}$ , $m ∠ B = 64^{\circ}$ and $m ∠ C = 62^{\circ}$ . List the sides shortest first. In a triangle, $m ∠ A = 45^{\circ}$ , $m ∠ B = 66^{\circ}$ and $m ∠ C = 69^{\circ}$ . List the sides shortest first. A triangle has $a = 19$ , $b = 17$ , $c = 15$ . List the angles smallest first. A triangle has $a = 22$ , $b = 15$ , $c = 24$ . List the angles smallest first. In a triangle, $m ∠ A = 68^{\circ}$ , $m ∠ B = 53^{\circ}$ and $m ∠ C = 59^{\circ}$ . List the sides shortest first. A triangle has $a = 24$ , $b = 18$ , $c = 23$ . List the angles smallest first. In a triangle, $m ∠ A = 70^{\circ}$ , $m ∠ B = 65^{\circ}$ and $m ∠ C = 45^{\circ}$ . List the sides shortest first. Compare sides and angles in a triangle In $△ J K L$ , $K L = 7$ , $J L = 5$ , $J K = 11$ . Name the largest angle. In $△ X Y Z$ , $Y Z = 16$ , $X Z = 6$ , $X Y = 15$ . Name the largest angle. In $△ R S T$ , $m ∠ R = 20^{\circ}$ and $m ∠ S = 71^{\circ}$ . Name the shortest side. In $△ R S T$ , $m ∠ R = 41^{\circ}$ and $m ∠ S = 97^{\circ}$ . Name the longest side. In $△ P Q R$ , $Q R = 20$ , $P R = 17$ , $P Q = 7$ . Name the largest angle. In $△ D E F$ , $E F = 12$ , $D F = 18$ , $D E = 10$ . Name the smallest angle. In $△ A B C$ , $m ∠ A = 54^{\circ}$ and $m ∠ B = 59^{\circ}$ . Name the longest side. In $△ P Q R$ , $Q R = 8$ , $P R = 10$ , $P Q = 4$ . Name the largest angle. In $△ J K L$ , $K L = 20$ , $J L = 15$ , $J K = 17$ . Name the smallest angle. In $△ A B C$ , $m ∠ A = 35^{\circ}$ and $m ∠ B = 88^{\circ}$ . Name the shortest side. Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Inequalities in One Triangle

Date Period

Order or name the sides or angles as asked.

Order the sides or angles
In a triangle, $m ∠ A = 51^{\circ}$ , $m ∠ B = 20^{\circ}$ and $m ∠ C = 109^{\circ}$ . List the sides shortest first.
A triangle has $a = 8$ , $b = 10$ , $c = 11$ . List the angles smallest first.
A triangle has $a = 22$ , $b = 27$ , $c = 23$ . List the angles smallest first.
In a triangle, $m ∠ A = 54^{\circ}$ , $m ∠ B = 64^{\circ}$ and $m ∠ C = 62^{\circ}$ . List the sides shortest first.
In a triangle, $m ∠ A = 45^{\circ}$ , $m ∠ B = 66^{\circ}$ and $m ∠ C = 69^{\circ}$ . List the sides shortest first.
A triangle has $a = 19$ , $b = 17$ , $c = 15$ . List the angles smallest first.
A triangle has $a = 22$ , $b = 15$ , $c = 24$ . List the angles smallest first.
In a triangle, $m ∠ A = 68^{\circ}$ , $m ∠ B = 53^{\circ}$ and $m ∠ C = 59^{\circ}$ . List the sides shortest first.
A triangle has $a = 24$ , $b = 18$ , $c = 23$ . List the angles smallest first.
In a triangle, $m ∠ A = 70^{\circ}$ , $m ∠ B = 65^{\circ}$ and $m ∠ C = 45^{\circ}$ . List the sides shortest first.

Compare sides and angles in a triangle
In $△ J K L$ , $K L = 7$ , $J L = 5$ , $J K = 11$ . Name the largest angle.
In $△ X Y Z$ , $Y Z = 16$ , $X Z = 6$ , $X Y = 15$ . Name the largest angle.
In $△ R S T$ , $m ∠ R = 20^{\circ}$ and $m ∠ S = 71^{\circ}$ . Name the shortest side.
In $△ R S T$ , $m ∠ R = 41^{\circ}$ and $m ∠ S = 97^{\circ}$ . Name the longest side.
In $△ P Q R$ , $Q R = 20$ , $P R = 17$ , $P Q = 7$ . Name the largest angle.
In $△ D E F$ , $E F = 12$ , $D F = 18$ , $D E = 10$ . Name the smallest angle.
In $△ A B C$ , $m ∠ A = 54^{\circ}$ and $m ∠ B = 59^{\circ}$ . Name the longest side.
In $△ P Q R$ , $Q R = 8$ , $P R = 10$ , $P Q = 4$ . Name the largest angle.
In $△ J K L$ , $K L = 20$ , $J L = 15$ , $J K = 17$ . Name the smallest angle.
In $△ A B C$ , $m ∠ A = 35^{\circ}$ and $m ∠ B = 88^{\circ}$ . Name the shortest side.



Sigma Prep · sigmaprep.io/worksheets Name Inequalities in One TriangleAnswer keyVersion 1 Date Period Order or name the sides or angles as asked. Order the sides or angles In a triangle, $m ∠ A = 51^{\circ}$ , $m ∠ B = 20^{\circ}$ and $m ∠ C = 109^{\circ}$ . List the sides shortest first. $b, a, c$ A triangle has $a = 8$ , $b = 10$ , $c = 11$ . List the angles smallest first. $A, B, C$ A triangle has $a = 22$ , $b = 27$ , $c = 23$ . List the angles smallest first. $A, C, B$ In a triangle, $m ∠ A = 54^{\circ}$ , $m ∠ B = 64^{\circ}$ and $m ∠ C = 62^{\circ}$ . List the sides shortest first. $a, c, b$ In a triangle, $m ∠ A = 45^{\circ}$ , $m ∠ B = 66^{\circ}$ and $m ∠ C = 69^{\circ}$ . List the sides shortest first. $a, b, c$ A triangle has $a = 19$ , $b = 17$ , $c = 15$ . List the angles smallest first. $C, B, A$ A triangle has $a = 22$ , $b = 15$ , $c = 24$ . List the angles smallest first. $B, A, C$ In a triangle, $m ∠ A = 68^{\circ}$ , $m ∠ B = 53^{\circ}$ and $m ∠ C = 59^{\circ}$ . List the sides shortest first. $b, c, a$ A triangle has $a = 24$ , $b = 18$ , $c = 23$ . List the angles smallest first. $B, C, A$ In a triangle, $m ∠ A = 70^{\circ}$ , $m ∠ B = 65^{\circ}$ and $m ∠ C = 45^{\circ}$ . List the sides shortest first. $c, b, a$ Compare sides and angles in a triangle In $△ J K L$ , $K L = 7$ , $J L = 5$ , $J K = 11$ . Name the largest angle. $∠ L$ In $△ X Y Z$ , $Y Z = 16$ , $X Z = 6$ , $X Y = 15$ . Name the largest angle. $∠ X$ In $△ R S T$ , $m ∠ R = 20^{\circ}$ and $m ∠ S = 71^{\circ}$ . Name the shortest side. $\overline{S T}$ In $△ R S T$ , $m ∠ R = 41^{\circ}$ and $m ∠ S = 97^{\circ}$ . Name the longest side. $\overline{R T}$ In $△ P Q R$ , $Q R = 20$ , $P R = 17$ , $P Q = 7$ . Name the largest angle. $∠ P$ In $△ D E F$ , $E F = 12$ , $D F = 18$ , $D E = 10$ . Name the smallest angle. $∠ F$ In $△ A B C$ , $m ∠ A = 54^{\circ}$ and $m ∠ B = 59^{\circ}$ . Name the longest side. $\overline{A B}$ In $△ P Q R$ , $Q R = 8$ , $P R = 10$ , $P Q = 4$ . Name the largest angle. $∠ Q$ In $△ J K L$ , $K L = 20$ , $J L = 15$ , $J K = 17$ . Name the smallest angle. $∠ K$ In $△ A B C$ , $m ∠ A = 35^{\circ}$ and $m ∠ B = 88^{\circ}$ . Name the shortest side. $\overline{B C}$ 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 or name the sides or angles as asked.

Order the sides or angles
In a triangle, $m ∠ A = 51^{\circ}$ , $m ∠ B = 20^{\circ}$ and $m ∠ C = 109^{\circ}$ . List the sides shortest first. $b, a, c$
A triangle has $a = 8$ , $b = 10$ , $c = 11$ . List the angles smallest first. $A, B, C$
A triangle has $a = 22$ , $b = 27$ , $c = 23$ . List the angles smallest first. $A, C, B$
In a triangle, $m ∠ A = 54^{\circ}$ , $m ∠ B = 64^{\circ}$ and $m ∠ C = 62^{\circ}$ . List the sides shortest first. $a, c, b$
In a triangle, $m ∠ A = 45^{\circ}$ , $m ∠ B = 66^{\circ}$ and $m ∠ C = 69^{\circ}$ . List the sides shortest first. $a, b, c$
A triangle has $a = 19$ , $b = 17$ , $c = 15$ . List the angles smallest first. $C, B, A$
A triangle has $a = 22$ , $b = 15$ , $c = 24$ . List the angles smallest first. $B, A, C$
In a triangle, $m ∠ A = 68^{\circ}$ , $m ∠ B = 53^{\circ}$ and $m ∠ C = 59^{\circ}$ . List the sides shortest first. $b, c, a$
A triangle has $a = 24$ , $b = 18$ , $c = 23$ . List the angles smallest first. $B, C, A$
In a triangle, $m ∠ A = 70^{\circ}$ , $m ∠ B = 65^{\circ}$ and $m ∠ C = 45^{\circ}$ . List the sides shortest first. $c, b, a$

Compare sides and angles in a triangle
In $△ J K L$ , $K L = 7$ , $J L = 5$ , $J K = 11$ . Name the largest angle. $∠ L$
In $△ X Y Z$ , $Y Z = 16$ , $X Z = 6$ , $X Y = 15$ . Name the largest angle. $∠ X$
In $△ R S T$ , $m ∠ R = 20^{\circ}$ and $m ∠ S = 71^{\circ}$ . Name the shortest side. $\overline{S T}$
In $△ R S T$ , $m ∠ R = 41^{\circ}$ and $m ∠ S = 97^{\circ}$ . Name the longest side. $\overline{R T}$
In $△ P Q R$ , $Q R = 20$ , $P R = 17$ , $P Q = 7$ . Name the largest angle. $∠ P$
In $△ D E F$ , $E F = 12$ , $D F = 18$ , $D E = 10$ . Name the smallest angle. $∠ F$
In $△ A B C$ , $m ∠ A = 54^{\circ}$ and $m ∠ B = 59^{\circ}$ . Name the longest side. $\overline{A B}$
In $△ P Q R$ , $Q R = 8$ , $P R = 10$ , $P Q = 4$ . Name the largest angle. $∠ Q$
In $△ J K L$ , $K L = 20$ , $J L = 15$ , $J K = 17$ . Name the smallest angle. $∠ K$
In $△ A B C$ , $m ∠ A = 35^{\circ}$ and $m ∠ B = 88^{\circ}$ . Name the shortest side. $\overline{B C}$

How to do these

$A = 40^{\circ},$ $B = 60^{\circ},$ $C = 80^{\circ}$

Side a faces angle A, and so on.
The angles go 40, 60, 80.
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.

What you can put on this worksheet

Ordering sides and angles: In a triangle, $m ∠ A = 47^{\circ}$ , $m ∠ B = 48^{\circ}$ and $m ∠ C = 85^{\circ}$ . List the sides shortest first. → $a, b, c$
Name the largest or smallest: In $△ X Y Z$ , $Y Z = 13$ , $X Z = 16$ , $X Y = 4$ . Name the largest angle. → $∠ Y$
The range an angle can take: In $△ P Q R$ , $\overline{Q R}$ is the shortest side and $m ∠ Q = 57^{\circ}$ . What values can $m ∠ P$ take? → $0^{\circ} < m ∠ P < 57^{\circ}$
Ordering, read off a drawing: List the angles from smallest to largest. — a triangle with its vertices named, labeled 12, 7, 11, X, Y, Z → $∠ X, ∠ Y, ∠ Z$

Questions about these worksheets