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.

Grade 11 Math GeometryTriangle Inequality Theorem

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Multiple ChoiceFill in the Blanks2 Short AnswerTrue / False

Standards

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

Topics

MathGeometryTriangle Inequality TheoremGrade 11

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 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?