Triangle Inequality Theorem Worksheets

What is Triangle Inequality Theorem? 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 the triangle inequality theorem. The triangle inequality theorem 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.

  • Basic Lesson

    Guides students through solving Triangle Inequality Theorem problems. Lengths 2, 6, 5 could represent the measures of the sides of a triangle? As sum of the lengths of any two sides of a triangle must be greater than the third side.

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  • Intermediate Lesson

    Demonstrates the concept of advanced skills while solving Triangle Inequality Theorem. Two sides of an isosceles triangles measure 2 and 7. What is the possible value of third side? In isosceles triangle, any two sides must be congruent to each other.

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  • Independent Practice 1

    A really great activity for allowing students to understand the concepts of the Triangle Inequality Theorem.

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  • Independent Practice 2

    Students use Triangle Inequality Theorem in 20 assorted problems. The answers can be found below.

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  • Homework Worksheet

    Students are provided with 12 problems to achieve the concepts of Triangle Inequality Theorem.

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  • Skill Quiz

    This tests the students ability to understand the use and application of the triangle inequality theorem.

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  • Answer Key

    Answers for all lessons and independent practice.

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Great Geometry Quotes

“Everything tries to be round.”-- Black Elk