# ResourceMAP - The Pythagorean Theorem and the Distance Formula - Teacher Edition

### Author: Gary Froelich

ResourceMAP modules are relatively short and designed for flexible implementation; that is, they can be used in regular classes as well as in special test-preparation settings. Each module contains a set of contextual problems in several formats: multi-part open response, short response, and multiple-choice. Accompanying the problem set are tip sheets that serve several purposes including lists of formulas, calculator instruction, and brief reviews of the module's underlying mathematics. Also provided are teacher notes (the module purpose, the mathematical focus, and implementation commentary), answers to all problems, and (in a few cases) handout masters. **The Pythagorean Theorem and the Distance Formula**

The Pythagorean theorem has many applications. It can be used to find missing

lengths and distances as you will see in the computer-networking problem that

follows. It can also be used to decide if an angle is a right angle.

**I. Purpose**

• To review the Pythagorean theorem and its converse

• To use the Pythagorean theorem to calculate the length of a missing side of a

right triangle

• To use the converse of the Pythagorean theorem to determine whether a

triangle is a right triangle

• To use the distance formula to determine distances between points on a

coordinate grid

**II. Mathematical Focus**

• Pythagorean theorem and its converse

• Distance formula

**III. Tip Sheet**

One Tip Sheet accompanies this module. It includes

• A statement of the Pythagorean theorem and examples of its use

• A statement of the converse of the Pythagorean theorem and an example of

its use

• A statement of the distance formula and an example of its use

#### Mathematics Topics:

#### Application Areas:

#### Prerequisites:

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