Classifying triangles worksheet for Pre-Algebra

In Pre-Algebra, classifying triangles means naming them by sides (scalene, isosceles, equilateral) and by angles (acute, right, obtuse). Some questions give all three angles. Others give the vertices on a grid, so you find the side lengths first and compare them.

Also taught in Geometry, at its own level and with its own examples.

Not quite the one you need? Same words, different skill:

Angles in a Triangle (Pre-Algebra). The third angle, and exterior angles.
Isosceles and Equilateral Triangles (Geometry). Equal sides mean equal angles.
The Exterior Angle Theorem (Geometry). An exterior angle equals the two far interior ones.

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



Sigma Prep · sigmaprep.io/worksheets Name Classifying Triangles Date Period Classify each triangle. Classify the triangle The angles of a triangle measure $52^{\circ}$ , $38^{\circ}$ and $90^{\circ}$ . Is it acute, right or obtuse? Classify the triangle by its sides. A triangle has sides $19$ , $20$ and $3$ . Classify it by its sides. Classify the triangle by its angles. The sides of a triangle measure $9$ , $9$ and $9$ . Is it scalene, isosceles or equilateral? In $△ A B C$ , $m ∠ A = 26^{\circ}$ , $m ∠ B = 34^{\circ}$ and $m ∠ C = 120^{\circ}$ . Classify the triangle by its angles. In $△ P Q R$ , $P Q = 10$ , $Q R = 5$ and $R P = 10$ . Classify $△ P Q R$ by its sides. A triangle has angles $90^{\circ}$ , $66^{\circ}$ and $24^{\circ}$ . Classify it by its angles. Classify the triangle by its sides. Classify the triangle by its angles. Classify a triangle from its vertices Classify the triangle with vertices $(- 4, 2)$ , $(- 6, 5)$ and $(- 7, 0)$ by its sides and by its angles. Classify the triangle with vertices $(- 4, - 5)$ , $(4, - 5)$ and $(0, - 10)$ by its sides and by its angles. Classify the triangle with vertices $(3, 0)$ , $(10, - 1)$ and $(2, 3)$ by its sides and by its angles. Classify the triangle with vertices $(- 5, - 1)$ , $(- 3, 1)$ and $(- 9, 3)$ by its sides and by its angles. Classify the triangle with vertices $(1, - 4)$ , $(1, 0)$ and $(2, - 2)$ by its sides and by its angles. Classify the triangle with vertices $(1, - 3)$ , $(1, 1)$ and $(- 3, - 1)$ by its sides and by its angles. Classify the triangle with vertices $(3, 1)$ , $(1, 2)$ and $(0, - 5)$ by its sides and by its angles. Classify the triangle with vertices $(1, 2)$ , $(4, 3)$ and $(- 2, 11)$ by its sides and by its angles. Classify the triangle with vertices $(0, - 1)$ , $(0, 5)$ and $(- 5, 2)$ by its sides and by its angles. Classify the triangle with vertices $(- 1, 3)$ , $(- 5, 5)$ and $(- 3, - 1)$ by its sides and by its angles. Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Classifying Triangles

Date Period

Classify each triangle.

Classify the triangle
The angles of a triangle measure $52^{\circ}$ , $38^{\circ}$ and $90^{\circ}$ . Is it acute, right or obtuse?
Classify the triangle by its sides.
A triangle has sides $19$ , $20$ and $3$ . Classify it by its sides.
Classify the triangle by its angles.
The sides of a triangle measure $9$ , $9$ and $9$ . Is it scalene, isosceles or equilateral?
In $△ A B C$ , $m ∠ A = 26^{\circ}$ , $m ∠ B = 34^{\circ}$ and $m ∠ C = 120^{\circ}$ . Classify the triangle by its angles.
In $△ P Q R$ , $P Q = 10$ , $Q R = 5$ and $R P = 10$ . Classify $△ P Q R$ by its sides.
A triangle has angles $90^{\circ}$ , $66^{\circ}$ and $24^{\circ}$ . Classify it by its angles.
Classify the triangle by its sides.
Classify the triangle by its angles.

Classify a triangle from its vertices
Classify the triangle with vertices $(- 4, 2)$ , $(- 6, 5)$ and $(- 7, 0)$ by its sides and by its angles.
Classify the triangle with vertices $(- 4, - 5)$ , $(4, - 5)$ and $(0, - 10)$ by its sides and by its angles.
Classify the triangle with vertices $(3, 0)$ , $(10, - 1)$ and $(2, 3)$ by its sides and by its angles.
Classify the triangle with vertices $(- 5, - 1)$ , $(- 3, 1)$ and $(- 9, 3)$ by its sides and by its angles.
Classify the triangle with vertices $(1, - 4)$ , $(1, 0)$ and $(2, - 2)$ by its sides and by its angles.
Classify the triangle with vertices $(1, - 3)$ , $(1, 1)$ and $(- 3, - 1)$ by its sides and by its angles.
Classify the triangle with vertices $(3, 1)$ , $(1, 2)$ and $(0, - 5)$ by its sides and by its angles.
Classify the triangle with vertices $(1, 2)$ , $(4, 3)$ and $(- 2, 11)$ by its sides and by its angles.
Classify the triangle with vertices $(0, - 1)$ , $(0, 5)$ and $(- 5, 2)$ by its sides and by its angles.
Classify the triangle with vertices $(- 1, 3)$ , $(- 5, 5)$ and $(- 3, - 1)$ by its sides and by its angles.



Sigma Prep · sigmaprep.io/worksheets Name Classifying TrianglesAnswer keyVersion 2 Date Period Classify each triangle. Classify the triangle The angles of a triangle measure $52^{\circ}$ , $38^{\circ}$ and $90^{\circ}$ . Is it acute, right or obtuse?Right Classify the triangle by its sides.Isosceles A triangle has sides $19$ , $20$ and $3$ . Classify it by its sides.Scalene Classify the triangle by its angles.Obtuse The sides of a triangle measure $9$ , $9$ and $9$ . Is it scalene, isosceles or equilateral?Equilateral In $△ A B C$ , $m ∠ A = 26^{\circ}$ , $m ∠ B = 34^{\circ}$ and $m ∠ C = 120^{\circ}$ . Classify the triangle by its angles.Obtuse In $△ P Q R$ , $P Q = 10$ , $Q R = 5$ and $R P = 10$ . Classify $△ P Q R$ by its sides.Isosceles A triangle has angles $90^{\circ}$ , $66^{\circ}$ and $24^{\circ}$ . Classify it by its angles.Right Classify the triangle by its sides.Scalene Classify the triangle by its angles.Right Classify a triangle from its vertices Classify the triangle with vertices $(- 4, 2)$ , $(- 6, 5)$ and $(- 7, 0)$ by its sides and by its angles.Isosceles, right Classify the triangle with vertices $(- 4, - 5)$ , $(4, - 5)$ and $(0, - 10)$ by its sides and by its angles.Isosceles, acute Classify the triangle with vertices $(3, 0)$ , $(10, - 1)$ and $(2, 3)$ by its sides and by its angles.Scalene, obtuse Classify the triangle with vertices $(- 5, - 1)$ , $(- 3, 1)$ and $(- 9, 3)$ by its sides and by its angles.Scalene, right Classify the triangle with vertices $(1, - 4)$ , $(1, 0)$ and $(2, - 2)$ by its sides and by its angles.Isosceles, obtuse Classify the triangle with vertices $(1, - 3)$ , $(1, 1)$ and $(- 3, - 1)$ by its sides and by its angles.Isosceles, acute Classify the triangle with vertices $(3, 1)$ , $(1, 2)$ and $(0, - 5)$ by its sides and by its angles.Scalene, right Classify the triangle with vertices $(1, 2)$ , $(4, 3)$ and $(- 2, 11)$ by its sides and by its angles.Scalene, right Classify the triangle with vertices $(0, - 1)$ , $(0, 5)$ and $(- 5, 2)$ by its sides and by its angles.Isosceles, acute Classify the triangle with vertices $(- 1, 3)$ , $(- 5, 5)$ and $(- 3, - 1)$ by its sides and by its angles.Isosceles, right Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Classifying TrianglesAnswer keyVersion 2

Date Period

Classify each triangle.

Classify the triangle
The angles of a triangle measure $52^{\circ}$ , $38^{\circ}$ and $90^{\circ}$ . Is it acute, right or obtuse?Right
Classify the triangle by its sides.Isosceles
A triangle has sides $19$ , $20$ and $3$ . Classify it by its sides.Scalene
Classify the triangle by its angles.Obtuse
The sides of a triangle measure $9$ , $9$ and $9$ . Is it scalene, isosceles or equilateral?Equilateral
In $△ A B C$ , $m ∠ A = 26^{\circ}$ , $m ∠ B = 34^{\circ}$ and $m ∠ C = 120^{\circ}$ . Classify the triangle by its angles.Obtuse
In $△ P Q R$ , $P Q = 10$ , $Q R = 5$ and $R P = 10$ . Classify $△ P Q R$ by its sides.Isosceles
A triangle has angles $90^{\circ}$ , $66^{\circ}$ and $24^{\circ}$ . Classify it by its angles.Right
Classify the triangle by its sides.Scalene
Classify the triangle by its angles.Right

Classify a triangle from its vertices
Classify the triangle with vertices $(- 4, 2)$ , $(- 6, 5)$ and $(- 7, 0)$ by its sides and by its angles.Isosceles, right
Classify the triangle with vertices $(- 4, - 5)$ , $(4, - 5)$ and $(0, - 10)$ by its sides and by its angles.Isosceles, acute
Classify the triangle with vertices $(3, 0)$ , $(10, - 1)$ and $(2, 3)$ by its sides and by its angles.Scalene, obtuse
Classify the triangle with vertices $(- 5, - 1)$ , $(- 3, 1)$ and $(- 9, 3)$ by its sides and by its angles.Scalene, right
Classify the triangle with vertices $(1, - 4)$ , $(1, 0)$ and $(2, - 2)$ by its sides and by its angles.Isosceles, obtuse
Classify the triangle with vertices $(1, - 3)$ , $(1, 1)$ and $(- 3, - 1)$ by its sides and by its angles.Isosceles, acute
Classify the triangle with vertices $(3, 1)$ , $(1, 2)$ and $(0, - 5)$ by its sides and by its angles.Scalene, right
Classify the triangle with vertices $(1, 2)$ , $(4, 3)$ and $(- 2, 11)$ by its sides and by its angles.Scalene, right
Classify the triangle with vertices $(0, - 1)$ , $(0, 5)$ and $(- 5, 2)$ by its sides and by its angles.Isosceles, acute
Classify the triangle with vertices $(- 1, 3)$ , $(- 5, 5)$ and $(- 3, - 1)$ by its sides and by its angles.Isosceles, right

How to do these

Classify the triangle with vertices $(1, 1)$ , $(5, 1)$ and $(3, 4)$ by its sides and by its angles

From (1, 1) to (5, 1) is 4. Each slanted side is √(2² + 3²) = √13.
Two sides are equal, so it is isosceles.
The longest side squared is 16, less than 13 + 13 = 26, so the largest angle is acute.

The answer is Isosceles, acute.

Where students go wrong

Calling a triangle acute because two of its angles are acute. Every triangle has at least two acute angles, so the largest angle decides: 90° makes it right, and anything over 90° makes it obtuse.

Also called triangle classification, types of triangles or acute obtuse right.

What you can put on this worksheet

By sides and by angles: Classify the triangle by its sides. — a triangle with two equal sides, labeled 12, 12, 7 → Isosceles
From the vertices: Classify the triangle with vertices $(0, 1)$ , $(2, 1)$ and $(3, 4)$ by its sides. → Scalene
From the marks, from a labelled drawing, or not possible: Classify the triangle by its sides and by its angles. — a triangle with tick marks on its sides, labeled 67°, 67° → Isosceles acute
Sides and angles, from the angles alone: What kind of triangle has angles of $46^{\circ}$ , $90^{\circ}$ and $44^{\circ}$ ? Give its side type and its angle type. → Scalene right

Questions about these worksheets

Yes. Every classifying triangles 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.

Pre-Algebra is usually taken around 7th or 8th 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 classifying triangles 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.

You pick from 4: by sides and by angles, from the vertices, from the marks, from a labelled drawing, or not possible and sides and angles, from the angles alone. Tick as many as you want and set how many of each, or let it spread them evenly.

Calling a triangle acute because two of its angles are. It only takes one angle of 90 or more to make it right or obtuse, so the largest angle is the only one worth checking.

Classifying triangles worksheet for Pre-Algebra

Classify the triangle

Classify a triangle from its vertices

Classify the triangle

Classify a triangle from its vertices

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these classifying triangles worksheets free?+

Do the classifying triangles worksheets come with an answer key?+

Are these classifying triangles worksheets printable?+

What grade are these classifying triangles worksheets for?+

Can I get a different version of the same classifying triangles worksheet?+

Is this a free alternative to Kuta Software for classifying triangles?+

Can I choose how hard the classifying triangles questions are?+

What kinds of question are on a classifying triangles worksheet?+

What do students get wrong with classifying triangles?+