Converse of Pythagorean Theorem Worksheet

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Examples, solutions, videos, and worksheets to help Grade 8 students learn how to apply the converse of the Pythagorean Theorem to determine whether a triangle is a right triangle.

How to use the Converse of the Pythagorean Theorem?

The converse of the Pythagorean Theorem states:
If the square of the length of the longest side of a triangle (hypotenuse) is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

In other words, if you have a triangle with sides of lengths 𝑎, 𝑏, and 𝑐 (where 𝑐 is the longest side), and if:
𝑐² = 𝑎² + 𝑏²
then the triangle is a right triangle.

How It Works:

• The regular Pythagorean Theorem tells us that if a triangle is a right triangle, the equation 𝑐² = 𝑎² + 𝑏² holds.
• The converse tells us that if the equation 𝑐² = 𝑎² + 𝑏² holds, then the triangle must be a right triangle.

Have a look at this video if you need to review how to use the converse of the Pythagorean Theorem.

• Converse of the Pythagorean Theorem

Click on the following worksheet to get a printable pdf document.
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More Converse of Pythagorean Theorem Worksheet Worksheets

Printable
(Answers on the second page.)
Converse of Pythagorean Theorem Worksheet #1
Converse of Pythagorean Theorem Worksheet #2
Converse of Pythagorean Theorem Worksheet #3

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