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More lessons for Grade 7 and Grade 8

Math Worksheets

Examples, solutions, videos, worksheets, stories, and songs to help Grade 8 students learn about the triangle inequality theorem.

The Triangle Inequality theorem states that

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

**Triangle Inequality**

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. To find a range of values for the third side when given two lengths, write two inequalities: one inequality that assumes the larger value given is the longest side in the triangle and one inequality that assumes that the third side is the longest side in the triangle. Combine the two inequalities for the final answer.

**How to determine the triangle side inequalities?**
**Description of the Triangle Inequality**

**Triangle Inequality Theorem**

Intuition behind the triangle inequality theorem
**Triangle Side and Angle Inequalities**

In any triangle, the largest angle is opposite the largest side (the opposite side of an angle is the side that does not form the angle). The shortest angle is opposite the shortest side. Therefore, the angle measures can be used to list the size order of the sides. The converse is also true: the lengths of the sides can be used to order the relative size of the angles. Triangle side and angle inequalities are important when solving proofs.

**How to determine the relationship between the side inequalities and angle inequalities in a triangle?**

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More lessons for Grade 7 and Grade 8

Math Worksheets

Examples, solutions, videos, worksheets, stories, and songs to help Grade 8 students learn about the triangle inequality theorem.

The Triangle Inequality theorem states that

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. To find a range of values for the third side when given two lengths, write two inequalities: one inequality that assumes the larger value given is the longest side in the triangle and one inequality that assumes that the third side is the longest side in the triangle. Combine the two inequalities for the final answer.

Intuition behind the triangle inequality theorem

In any triangle, the largest angle is opposite the largest side (the opposite side of an angle is the side that does not form the angle). The shortest angle is opposite the shortest side. Therefore, the angle measures can be used to list the size order of the sides. The converse is also true: the lengths of the sides can be used to order the relative size of the angles. Triangle side and angle inequalities are important when solving proofs.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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