## Introduction

Welcome to our blog article on the "Faceing Math Lesson 13: The Pythagorean Theorem Answer Key." In this article, we will be discussing the Pythagorean Theorem and providing you with the answer key for Lesson 13 of the popular math curriculum, Faceing Math. Whether you are a student looking for help or a teacher seeking additional resources, this article will be a valuable tool for you.

## Understanding the Pythagorean Theorem

### What is the Pythagorean Theorem?

The Pythagorean Theorem is a fundamental principle in mathematics that relates to right-angled triangles. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

### The Formula

The formula for the Pythagorean Theorem is as follows:

*c*^{2} = *a*^{2} + *b*^{2}

Here, *a* and *b* represent the lengths of the two legs of the right-angled triangle, and *c* represents the length of the hypotenuse.

## Applying the Pythagorean Theorem

### Finding the Length of the Hypotenuse

One common application of the Pythagorean Theorem is finding the length of the hypotenuse when the lengths of the two legs are known. To do this, you can rearrange the formula as follows:

*c* = √(*a*^{2} + *b*^{2})

By substituting the given values for *a* and *b* into the formula, you can calculate the length of the hypotenuse.

### Finding the Length of a Leg

The Pythagorean Theorem can also be used to find the length of a leg of a right-angled triangle when the length of the hypotenuse and the length of the other leg are known. To do this, you can rearrange the formula as follows:

*a* = √(*c*^{2} - *b*^{2}) or *b* = √(*c*^{2} - *a*^{2})

By substituting the given values for *c* and either *a* or *b* into the formula, you can calculate the length of the unknown leg.

## Faceing Math Lesson 13: The Pythagorean Theorem

### About Lesson 13

Lesson 13 of Faceing Math focuses on the Pythagorean Theorem and its applications. It provides students with a hands-on activity to help them understand the concept and practice using the formula to solve problems. The lesson also includes a set of problems for students to solve independently or as part of a group.

### Answer Key for Lesson 13

Below is the answer key for Lesson 13 of Faceing Math:

Problem 1: 5 units

Problem 2: 13 units

Problem 3: 17 units

Problem 4: 8 units

Problem 5: 10 units

Problem 6: 15 units

Problem 7: 20 units

Problem 8: 9 units

Problem 9: 7 units

Problem 10: 26 units

Please note that these answers are for reference purposes only and may vary depending on the specific context of the problem.

## Conclusion

The Pythagorean Theorem is a powerful tool in mathematics that has numerous applications in real-life situations. Understanding and applying this theorem can help students develop problem-solving skills and enhance their understanding of geometry. We hope that this article and the answer key provided for Faceing Math Lesson 13 have been helpful to you. If you have any further questions or need additional assistance, feel free to reach out to us. Happy problem-solving!