Triangle Inequality Theorem Worksheet
Grade 11 Math worksheet focusing on the Triangle Inequality Theorem, including identifying valid triangles, finding possible side lengths, and applying the theorem to solve problems.
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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 work for problems requiring calculations. Remember the Triangle Inequality Theorem states that 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 CANNOT form a triangle?
3 cm, 4 cm, 5 cm
6 cm, 8 cm, 10 cm
2 cm, 3 cm, 6 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
30 inches
6 inches
15 inches
3. The sum of the lengths of any two sides of a triangle must be than the length of the third side.
4. If the side lengths are 5, 8, and x, then the possible values for x are between and (exclusive).
5. A triangle has two sides with lengths 7 cm and 10 cm. Describe the range of possible lengths for the third side. Explain your reasoning.
6. A triangle can have side lengths of 1, 2, and 3.
True
False
7. If a triangle has side lengths a, b, and c, then a + b > c, a + c > b, and b + c > a must all be true.
True
False
8. Consider a triangle with sides (x + 2), (x + 3), and (x + 4). For what values of x can these side lengths form a valid triangle?
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