The Pythagorean Theorem can be written as follows:

It is important to note that

• The Pythagorean Theorem can only be used for right triangles, and
• the Pythagorean Theorem can be used to determine any missing side length of a right triangle if you know the lengths of the two remaining sides.

You will investigate detailed real-world applications of the Pythagorean Theorem in a later lesson.

Examine the figures shown below. Sort them into two categories: those whose labeled sides demonstrate the Pythagorean Theorem and those whose labeled sides do not demonstrate the Pythagorean Theorem.

Practice

Identify which of the following triangles has side lengths a, b, and c that correctly demonstrate the Pythagorean Theorem.

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Check Your Answer

Triangles I and III