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Back to Explain a proof of the Pythagorean Theorem and its converse — Problem 1 · Task Set 26

Exercises: Proving the Pythagorean Theorem and Its Converse

Work through each section in order. The theorem a2+b2=c2a^2 + b^2 = c^2 relates the legs aa and bb to the hypotenuse cc of a right triangle. Show your reasoning where indicated.

Grade 8·22 problems·~35 min·Common Core Math - Grade 8·container·8-g-b-6
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Recall / Warm-Up

These problems review skills you already know: parts of a right triangle, squares of numbers, and triangle angle sums.

A right triangle with the right angle at the bottom-left, sides labeled p (vertical leg), q (horizontal leg), and r (slanted side opposite the right angle).
1.

In the right triangle shown, which side is the hypotenuse?