Unit 5 Relationships in Triangles Homework 8 focuses on triangle inequalities. Students must understand the rules and principles of triangle inequalities before they can solve any related problems. Triangle inequalities are important for understanding the relationship between the sides of a triangle. They are essential for solving geometry problems.

## What Is a Triangle Inequality?

A triangle inequality is a statement that states the relationship between the sides of a triangle. It states that the sum of any two sides of a triangle must be greater than the length of the third side. This means that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This is the triangle inequality theorem.

## How to Use Triangle Inequalities to Solve Problems

When students are asked to solve problems related to triangle inequalities, they must first identify the triangle and its sides. After that, they must apply the triangle inequality theorem to the given triangle. Then, they must determine the relationships between the sides. This can be done by comparing the lengths of the sides and applying the triangle inequality theorem. Finally, they must solve the problem by finding the length of the third side.

## Examples of Triangle Inequalities

To better understand triangle inequalities, here are some examples. If the lengths of two sides of a triangle are 5 and 8, then the length of the third side must be greater than 3. If the lengths of two sides of a triangle are 4 and 12, then the length of the third side must be greater than 8. If the lengths of two sides of a triangle are 7 and 15, then the length of the third side must be greater than 8.

Unit 5 Relationships in Triangles Homework 8 is all about triangle inequalities. To solve problems related to triangle inequalities, students must first identify the triangle and its sides. Then, they must apply the triangle inequality theorem to the given triangle. By understanding and applying the triangle inequality theorem, students will be able to solve problems related to triangle inequalities.