Triangle Inequality Theorem Worksheet

Triangle Inequality Theorem

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?

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?

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.

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).

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?