Triangle Inequality Theorem Worksheet

Explore the Triangle Inequality Theorem with this Grade 6 worksheet, featuring questions on side length conditions and real-world applications.

Grade 6 Math GeometryTriangle Inequality Theorem

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Multiple ChoiceTrue / FalseFill in the BlanksShort Answer

Standards

CCSS.MATH.CONTENT.7.G.A.2

Topics

MathGeometryTrianglesTriangle Inequality TheoremGrade 6

6 sections · Free to use · Printable

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Triangle Inequality Theorem

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Read each question carefully and answer to the best of your ability. Remember the Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

1. Which set of side lengths CAN form a triangle?

2 cm, 3 cm, 6 cm

4 cm, 4 cm, 8 cm

5 cm, 7 cm, 10 cm

1 cm, 2 cm, 3 cm

2. If two sides of a triangle are 8 inches and 12 inches, which of the following could be the length of the third side?

3 inches

4 inches

15 inches

20 inches

3. A triangle can have side lengths of 10 cm, 10 cm, and 10 cm.

True

False

4. If you have two sticks of lengths 5 feet and 7 feet, you can always form a triangle with a third stick of any length.

True

False

5. According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be than the length of the third side.

6. If the sides of a triangle are a, b, and c, then a + b > c, a + c > b, and b + c > must all be true.

7. You are building a triangular garden. You have two sides that are 15 feet and 20 feet long. What is the range of possible lengths for the third side?

8. Examine the triangle below. Can a triangle be formed with the given side lengths? Explain your reasoning.