Converse of the Pythagorean theorem worksheet for Pre-Algebra

Pre-Algebra uses this as a quick follow-up to the Pythagorean theorem: given three whole-number sides, decide what kind of triangle they make. It comes down to squaring, adding and comparing. Right is the exact match; acute and obtuse are the two ways it can miss.

Also taught in Geometry and Algebra 1, each at its own level and with its own examples.

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

The Pythagorean Theorem (Pre-Algebra). A missing side, a word problem, or an area.
The Diagonal of a Box (Geometry). Pythagoras twice: across the base, then up.

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



Sigma Prep · sigmaprep.io/worksheets Name Converse of the Pythagorean Theorem Date Period Classify each triangle from its sides. What kind of triangle has sides $14, 8$ and $21$ : right, acute or obtuse? Right, acute or obtuse: a triangle with sides $9, 41$ and $40$ ? A triangle has sides $12, 16$ and $19$ . Right, acute or obtuse? Use the sides $20, 17$ and $6$ to say if the triangle is right, acute or obtuse. The sides of a triangle measure $34, 33$ and $21$ . Is it right, acute or obtuse? Classify the triangle with sides $30, 72$ and $78$ as right, acute or obtuse. Is a triangle with side lengths $7, 17$ and $20$ right, acute or obtuse? Use the sides $45, 24$ and $50$ to say if the triangle is right, acute or obtuse. The sides of a triangle measure $60, 87$ and $63$ . Is it right, acute or obtuse? What kind of triangle has sides $6, 5$ and $4$ : right, acute or obtuse? Right, acute or obtuse: a triangle with sides $24, 7$ and $25$ ? Classify the triangle with sides $26, 31$ and $10$ as right, acute or obtuse. A triangle has sides $20, 20$ and $36$ . Right, acute or obtuse? Is a triangle with side lengths $34, 34$ and $35$ right, acute or obtuse? What kind of triangle has sides $56, 58$ and $99$ : right, acute or obtuse? The sides of a triangle measure $20, 17$ and $12$ . Is it right, acute or obtuse? A triangle has sides $17, 36$ and $30$ . Right, acute or obtuse? Is a triangle with side lengths $11, 23$ and $22$ right, acute or obtuse? Classify the triangle with sides $16, 30$ and $34$ as right, acute or obtuse. Use the sides $11, 19$ and $21$ to say if the triangle is right, acute or obtuse. Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Converse of the Pythagorean Theorem

Date Period

Classify each triangle from its sides.

What kind of triangle has sides $14, 8$ and $21$ : right, acute or obtuse?
Right, acute or obtuse: a triangle with sides $9, 41$ and $40$ ?
A triangle has sides $12, 16$ and $19$ . Right, acute or obtuse?
Use the sides $20, 17$ and $6$ to say if the triangle is right, acute or obtuse.
The sides of a triangle measure $34, 33$ and $21$ . Is it right, acute or obtuse?
Classify the triangle with sides $30, 72$ and $78$ as right, acute or obtuse.
Is a triangle with side lengths $7, 17$ and $20$ right, acute or obtuse?
Use the sides $45, 24$ and $50$ to say if the triangle is right, acute or obtuse.
The sides of a triangle measure $60, 87$ and $63$ . Is it right, acute or obtuse?
What kind of triangle has sides $6, 5$ and $4$ : right, acute or obtuse?
Right, acute or obtuse: a triangle with sides $24, 7$ and $25$ ?
Classify the triangle with sides $26, 31$ and $10$ as right, acute or obtuse.
A triangle has sides $20, 20$ and $36$ . Right, acute or obtuse?
Is a triangle with side lengths $34, 34$ and $35$ right, acute or obtuse?
What kind of triangle has sides $56, 58$ and $99$ : right, acute or obtuse?
The sides of a triangle measure $20, 17$ and $12$ . Is it right, acute or obtuse?
A triangle has sides $17, 36$ and $30$ . Right, acute or obtuse?
Is a triangle with side lengths $11, 23$ and $22$ right, acute or obtuse?
Classify the triangle with sides $16, 30$ and $34$ as right, acute or obtuse.
Use the sides $11, 19$ and $21$ to say if the triangle is right, acute or obtuse.



Sigma Prep · sigmaprep.io/worksheets Name Converse of the Pythagorean TheoremAnswer keyVersion 2 Date Period Classify each triangle from its sides. What kind of triangle has sides $14, 8$ and $21$ : right, acute or obtuse?Obtuse Right, acute or obtuse: a triangle with sides $9, 41$ and $40$ ?Right A triangle has sides $12, 16$ and $19$ . Right, acute or obtuse?Acute Use the sides $20, 17$ and $6$ to say if the triangle is right, acute or obtuse.Obtuse The sides of a triangle measure $34, 33$ and $21$ . Is it right, acute or obtuse?Acute Classify the triangle with sides $30, 72$ and $78$ as right, acute or obtuse.Right Is a triangle with side lengths $7, 17$ and $20$ right, acute or obtuse?Obtuse Use the sides $45, 24$ and $50$ to say if the triangle is right, acute or obtuse.Acute The sides of a triangle measure $60, 87$ and $63$ . Is it right, acute or obtuse?Right What kind of triangle has sides $6, 5$ and $4$ : right, acute or obtuse?Acute Right, acute or obtuse: a triangle with sides $24, 7$ and $25$ ?Right Classify the triangle with sides $26, 31$ and $10$ as right, acute or obtuse.Obtuse A triangle has sides $20, 20$ and $36$ . Right, acute or obtuse?Obtuse Is a triangle with side lengths $34, 34$ and $35$ right, acute or obtuse?Acute What kind of triangle has sides $56, 58$ and $99$ : right, acute or obtuse?Obtuse The sides of a triangle measure $20, 17$ and $12$ . Is it right, acute or obtuse?Acute A triangle has sides $17, 36$ and $30$ . Right, acute or obtuse?Obtuse Is a triangle with side lengths $11, 23$ and $22$ right, acute or obtuse?Acute Classify the triangle with sides $16, 30$ and $34$ as right, acute or obtuse.Right Use the sides $11, 19$ and $21$ to say if the triangle is right, acute or obtuse.Acute Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Converse of the Pythagorean TheoremAnswer keyVersion 2

Date Period

Classify each triangle from its sides.

What kind of triangle has sides $14, 8$ and $21$ : right, acute or obtuse?Obtuse
Right, acute or obtuse: a triangle with sides $9, 41$ and $40$ ?Right
A triangle has sides $12, 16$ and $19$ . Right, acute or obtuse?Acute
Use the sides $20, 17$ and $6$ to say if the triangle is right, acute or obtuse.Obtuse
The sides of a triangle measure $34, 33$ and $21$ . Is it right, acute or obtuse?Acute
Classify the triangle with sides $30, 72$ and $78$ as right, acute or obtuse.Right
Is a triangle with side lengths $7, 17$ and $20$ right, acute or obtuse?Obtuse
Use the sides $45, 24$ and $50$ to say if the triangle is right, acute or obtuse.Acute
The sides of a triangle measure $60, 87$ and $63$ . Is it right, acute or obtuse?Right
What kind of triangle has sides $6, 5$ and $4$ : right, acute or obtuse?Acute
Right, acute or obtuse: a triangle with sides $24, 7$ and $25$ ?Right
Classify the triangle with sides $26, 31$ and $10$ as right, acute or obtuse.Obtuse
A triangle has sides $20, 20$ and $36$ . Right, acute or obtuse?Obtuse
Is a triangle with side lengths $34, 34$ and $35$ right, acute or obtuse?Acute
What kind of triangle has sides $56, 58$ and $99$ : right, acute or obtuse?Obtuse
The sides of a triangle measure $20, 17$ and $12$ . Is it right, acute or obtuse?Acute
A triangle has sides $17, 36$ and $30$ . Right, acute or obtuse?Obtuse
Is a triangle with side lengths $11, 23$ and $22$ right, acute or obtuse?Acute
Classify the triangle with sides $16, 30$ and $34$ as right, acute or obtuse.Right
Use the sides $11, 19$ and $21$ to say if the triangle is right, acute or obtuse.Acute

How to do these

A triangle has sides $10, 6, 9$ . Right, acute or obtuse?

The longest side is 10, even though it is listed first.
6² + 9² = 36 + 81 = 117.
10² = 100, and 117 is more than 100.

The answer is Acute.

Where students go wrong

Comparing the sides before squaring them. 6 + 9 is more than 10 for every triangle, so adding the plain sides tells you nothing; square first, then add.

Also called classifying triangles by sides, Pythagorean inequalities, is it a right triangle or Pythagorean triples.

What you can put on this worksheet

Right, acute or obtuse from the sides: Use the sides $8, 15$ and $16$ to say if the triangle is right, acute or obtuse. → Acute
Decimal or root sides, or read off a drawing: A triangle has sides $21, 6 \sqrt{10}, 9$ . Right, acute or obtuse? → Right

Questions about these worksheets

Yes. Every converse of the pythagorean 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.

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 converse of the pythagorean 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.

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 2: right, acute or obtuse from the sides and decimal or root sides, or read off a drawing. Tick as many as you want and set how many of each, or let it spread them evenly.

Squaring the wrong side on its own. The comparison only works with the longest side alone on one side of the equation.

Converse of the Pythagorean theorem worksheet for Pre-Algebra

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

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