Triangle Inequality Theorem Worksheet

Grade 10 math worksheet focusing on the Triangle Inequality Theorem, including identifying valid triangles, finding possible side lengths, and applying the theorem to real-world scenarios.

Grade 10 Math GeometryTriangle Inequality Theorem

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Includes

Multiple ChoiceFill in the Blanks2 Short AnswerTrue / False

Standards

CCSS.MATH.CONTENT.HSG.CO.C.10

Topics

GeometryTrianglesTriangle Inequality TheoremGrade 10

7 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. Show all your work for full credit.

1. Which set of side lengths CANNOT form a triangle?

3 cm, 4 cm, 5 cm

6 cm, 8 cm, 10 cm

2 cm, 5 cm, 7 cm

7 cm, 7 cm, 7 cm

2. If two sides of a triangle are 12 inches and 18 inches, which of the following could be the length of the third side?

5 inches

6 inches

29 inches

30 inches

3. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be than the length of the third side.

4. If the sides of a triangle are a, b, and c, then the following three inequalities must be true: a + b > c, a + c > b, and .

5. Determine if a triangle can be formed with side lengths of 8 m, 15 m, and 7 m. Justify your answer using the Triangle Inequality Theorem.

6. Two sides of a triangle have lengths 10 cm and 24 cm. What is the range of possible lengths for the third side?

7. A triangle has sides of length x, x + 3, and x + 6. Find all possible integer values of x that satisfy the Triangle Inequality Theorem.

8. A triangle with side lengths 1, 2, and 3 can exist.

True

False

9. If the sum of two sides of a triangle is equal to the third side, then a degenerate triangle is formed (a straight line).

True

False

10. Sarah is building a triangular garden. She has two fences that are 10 feet and 16 feet long. What are the possible whole number lengths for the third fence?