# Course 3 Chapter 5 Triangles And The Pythagorean Theorem Answers

## Introduction

In this article, we will be discussing the answers to course 3 chapter 5 triangles and the Pythagorean theorem. This chapter is an important one as it deals with the basic concepts of triangles and the Pythagorean theorem, which is an essential tool for solving problems related to triangles. By the end of this article, you will have a better understanding of the important concepts in this chapter.

### What are Triangles?

A triangle is a closed figure with three straight sides and three angles. Triangles come in different shapes and sizes, but the sum of the angles of any triangle is always 180 degrees. Triangles are used in many mathematical and real-world applications, such as architecture, engineering, and physics.

### The Pythagorean Theorem

The Pythagorean theorem is a fundamental concept in mathematics that states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) 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.

### How to Use the Pythagorean Theorem?

To use the Pythagorean theorem, we need to know the lengths of two sides of a right triangle. We can then use the theorem to find the length of the third side, which is the hypotenuse. For example, if we know the length of the two shorter sides of a right triangle are 3 and 4 units, we can use the Pythagorean theorem to find the length of the hypotenuse. The calculation would be as follows: hypotenuse^2 = 3^2 + 4^2 hypotenuse^2 = 9 + 16 hypotenuse^2 = 25 hypotenuse = √25 hypotenuse = 5 Therefore, the length of the hypotenuse is 5 units.

### Answers to Course 3 Chapter 5 Triangles and the Pythagorean Theorem

The answers to the questions in this chapter are as follows: 1. What is a triangle? Answer: A triangle is a closed figure with three straight sides and three angles. 2. What is the Pythagorean theorem? Answer: The Pythagorean theorem is a fundamental concept in mathematics that states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. 3. How do you use the Pythagorean theorem? Answer: To use the Pythagorean theorem, we need to know the lengths of two sides of a right triangle. We can then use the theorem to find the length of the third side, which is the hypotenuse. 4. What is the formula for the Pythagorean theorem? Answer: The formula for the Pythagorean theorem is a^2 + b^2 = c^2, where a and b are the lengths of the other two sides, and c is the length of the hypotenuse.

### Conclusion

In conclusion, the course 3 chapter 5 triangles and the Pythagorean theorem is an important chapter that deals with the basic concepts of triangles and the Pythagorean theorem. By understanding these concepts, you will be able to solve problems related to triangles and apply them in real-world situations. We hope that this article has helped you in understanding this chapter better.