Triangle Inequality Theorem Worksheet
Explore the Triangle Inequality Theorem with this Grade 7 worksheet, featuring questions on identifying valid triangles and determining possible side lengths.
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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, 5 cm, 9 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
20 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 a triangle has sides of length 7 units and 10 units, the third side 'x' must satisfy the inequality: < x < .
5. A triangle can have side lengths of 5 cm, 5 cm, and 10 cm.
True
False
6. If the sides of a triangle are a, b, and c, then a + b > c, a + c > b, and b + c > a must all be true.
True
False
7. A triangle has two sides with lengths 6 inches and 10 inches. Write an inequality that represents the possible lengths for the third side, x.
8. Can a triangle have side lengths of 15 ft, 8 ft, and 7 ft? Explain your reasoning using the Triangle Inequality Theorem.
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