Triangle Inequality Theorem Worksheet
A Grade 12 math worksheet focusing on the Triangle Inequality Theorem, including identifying valid triangles, determining possible side lengths, and working with algebraic expressions.
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Triangle Inequality Theorem
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Read each question carefully and apply the Triangle Inequality Theorem to determine the correct answers. Remember 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, 4, 5
6, 8, 10
2, 3, 6
7, 7, 7
2. If two sides of a triangle are 12 cm and 17 cm, which of the following could be the length of the third side?
4 cm
5 cm
29 cm
30 cm
3. For a triangle with side lengths a, b, and c, the Triangle Inequality Theorem states that a + b > c, b + c > a, and a + c > .
4. If the lengths of two sides of a triangle are 9 units and 15 units, the length of the third side must be greater than units and less than units.
5. A triangle has side lengths of (x + 2), (2x - 1), and (x + 5). Determine the possible range of values for x.
6. Can a triangle have side lengths of 4.5 inches, 6.2 inches, and 10.8 inches? Justify your answer using the Triangle Inequality Theorem.
7. A triangle with side lengths 1, 1, and 1 can be formed.
True
False
8. If the sum of two side lengths of a triangle is equal to the third side length, then a triangle can still be formed.
True
False
9. Consider a triangle with two sides measuring 8 units and 13 units. Let the third side be 's'. Write an inequality that represents the possible range of values for 's'.
10. Two sides of a triangle are 10 cm and 24 cm. If the third side is an integer, how many possible integer lengths are there for the third side?