## Introduction

Geometry is one of the most fundamental branches of mathematics, and special right triangles are an essential part of it. A special right triangle is a triangle with angles that have specific values. In this article, we will be focusing on the 45-45-90 special right triangle and its worksheet answer key.

## What is a 45-45-90 Special Right Triangle?

A 45-45-90 special right triangle is a right triangle that has two equal angles of 45 degrees each and one right angle of 90 degrees. The two equal sides of this triangle are called legs, while the third side, which is the longest, is called the hypotenuse.

## Properties of a 45-45-90 Special Right Triangle

Since the two legs of a 45-45-90 special right triangle are equal, the ratio of the length of the hypotenuse to each leg is sqrt(2). Therefore, if we know the length of one leg of the triangle, we can easily find the length of the other leg and the hypotenuse.

## Worksheet Questions and Answers

To practice working with 45-45-90 special right triangles, we can use worksheets that contain questions and answers. Here are some sample questions and answers:

1. Find the length of the hypotenuse of a 45-45-90 special right triangle with a leg length of 5.

Answer: The length of the hypotenuse is 5 * sqrt(2) = 7.07.

2. Find the length of one leg of a 45-45-90 special right triangle with a hypotenuse length of 10.

Answer: The length of one leg is 10 / sqrt(2) = 7.07.

3. Find the length of the hypotenuse of a 45-45-90 special right triangle with a leg length of 8.

Answer: The length of the hypotenuse is 8 * sqrt(2) = 11.31.

## Applications of 45-45-90 Special Right Triangles

45-45-90 special right triangles have many practical applications, especially in engineering and architecture. They are used to construct square shapes, as the two equal legs of the triangle can form the sides of a square, and the hypotenuse can form the diagonal of the square.

## Conclusion

In conclusion, understanding and being able to work with special right triangles is essential in geometry. The 45-45-90 special right triangle is one of the most common special right triangles, and knowing its properties can help us solve many problems in mathematics, engineering, and architecture. By using worksheets and practicing with sample questions and answers, we can improve our skills in working with 45-45-90 special right triangles.

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