These worksheets will teach your students how to use inequalities to determine triangle side length.

#### Triangle Inequality Theorem tells us that if you add any two sides of a triangle, they will be greater than the third side in length. The basic reason is that if that third side was longer, the two sides would never meet up. This can help us mathematically determine if in fact you have a legitimate triangle. In fact this is calculation is being performed hundreds of times each second that your mobile phone is looking for a signal.

We all are familiar with the fact that we need three line segments to form a triangle. But what most of us don't know that the three line segments used to form a triangle need to have a relationship among themselves. For instance, if you were given lines segments of measurements 3, 4,5, you can easily form a triangle out of it. On the other hand, you cannot form a triangle out of measurements 3,4, and 9. Therefore, you cannot create a triangle from any three segments; you need the three line segments in a relationship. That relationship is explained by this theorem. It basically states that the length of any side of the triangle should be shorter than the sum of the two segments added together. This shows that for creating a triangle, no side can not be longer than the lengths of sides combined. For example, we can easily create a triangle from lengths 3, 4, and 5 as these lengths don't satisfy the theorem. 4 + 5 = 9 and 3 < 9 : 3 + 4 = 7 and 5 < 7 : 3 + 5 = 8 and 4 < 8 It is clear that none of the line segment is longer than the two sides of the triangle. However, if we considered lengths 3, 4, and 9, we know that length 9 is longer than the sum of the two sides. 3 + 4 = 7 and 9 > 7. These worksheets explain how to use inequalities to determine the length of a triangle's sides. Please remind students how this skill basically relates to all work with triangles.

# Print Triangle Inequality Theorem Worksheets

## Lesson and Practice

Students will use inequalities to determine the length of a triangle's sides. A sample problem is solved and two practice problems are provided.

## Inequality Theorem Worksheet

Students are given inequalities and will determine the measure of the sides of triangles. Nine problems are provided.

## Theorem Practice Worksheet

Students will use inequality to find the measure of the sides of triangles. Nine problems are provided.

## Review and Practice Worksheets

This worksheet reviews how to use inequality to find the measure of the sides of triangles. On this page, a sample problem is solved and six practice problems are provided.

Students demonstrate their proficiency using inequalities to find the lengths of a triangle's sides. Nine problems are provided.

## Inequality Theorem Check Sheet

Students will find the lengths of side of triangles. Three problems are provided, and space is included for students to copy the correct answer when given.

## Working with Triangle Inequalities Lesson and Practice

Students will find the longest side of each described shape. A sample problem is solved and two practice problems are provided.

## Working with Them Worksheet

Students will use the measurements of angles to find the longest side of the triangles. Ten problems are provided.

## Solving Geometric Inequalities Practice

Students will find the longest side of each triangle based on information provided. Ten problems are provided.

## Review and Practice Page

This worksheet reviews how to use inequalities to find the length of the sides of triangles. A sample problem is solved and six practice problems are provided.

## Skill Quiz

Students demonstrate their proficiency using inequalities to find the length of triangle sides. Ten problems are provided.

## Skills Check

Students will find the lengths of the sides of the good old three sided shape. Three problems are provided, and space is included for students to copy the correct answer when given.