An Introduction to the Pythagorean Theorem

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For many middle school students, the Pythagorean theorem represents one of the most prevalent equations of geometry that must be mastered. Most teachers introduce the theorem to students following lessons on square roots, as an understanding of square roots is critical to solving a Pythagorean equation effectively. Using the theorem, students can solve for the length of the third side of a right triangle, assuming they have been provided the length for each of the remaining two sides.

The theorem states that when the square of both sides of a triangle are added together, individuals are left with the squared length of the triangle’s largest side, commonly referred to as the hypotenuse. Introductory Pythagorean equations provide two lengths and challenge students to solve for the remaining side, though the unknown side is not always the hypotenuse. Students must remember that the theorem can only be applied to triangles featuring a right angle.