Pythagorean Theorem Worksheet

The Pythagorean Theorem, a² + b² = c², describes the relationship between the lengths of the three sides of a right triangle. The theorem, which is likely the most famous theorem in mathematics, states that adding the squares of a right triangle’s leg lengths will equal the square of the hypotenuse length. Students will encounter this theorem in their math curriculum, on various standardized tests, and in real-world applications outside the classroom.

Outside the classroom there are many uses for the Pythagorean theorem. A common application is carpentry. Carpenters will often use the Pythagorean theorem to determine if a structure is square. To do this they will usually use a quick method called the 3:4:5 triangle. If a carpenter wants to make sure a wall is perpendicular to the floor, they will measure 4 feet up the wall and 3 feet across the floor. The distance between the end point of these two measurements should be 5 feet, if the wall is perpendicular to the floor. This worksheet is designed to help students practice working with this theorem.

The Pythagorean theorem worksheet maker creates worksheets with up to 9 right triangles on each. The student’s goal is to calculate the length of a triangles leg or hypotenuse when only 2 sides are known, using the theorem. The worksheets are randomly generated, so you can create multiple worksheets without repeating the same problem sets. The custom algorithm creates the triangles so that all the sides are whole numbers. This allows students to concentrate on the fundamentals of the theorem without worrying about rounding decimals. You can also customize what the students will solve for. You can select to have the students solve for the legs of the triangle, hypotenuse of the triangle, or both. After the worksheet has been customized to your preferences, you can download it as a PDF in US Letter or A4 format. Each PDF includes a matching answer key for the worksheet.