To determine which group of segments can form a triangle, we can use the triangle inequality theorem. This theorem states that for any three lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's apply this theorem to each option:
A. 3, 10, 14
- 3 + 10 = 13, which is not greater than 14.
Therefore, these lengths do not satisfy the triangle inequality theorem.
B. 8, 7, 13
- 8 + 7 = 15, which is greater than 13.
- 8 + 13 = 21, which is greater than 7.
- 7 + 13 = 20, which is greater than 8.
All three conditions are satisfied, so these lengths can form a triangle.
C. 3, 2, 5
- 3 + 2 = 5, which is not greater than 5.
Therefore, these lengths do not satisfy the triangle inequality theorem.
D. 20, 7, 13
- 20 + 7 = 27, which is greater than 13.
- 20 + 13 = 33, which is greater than 7.
- 7 + 13 = 20, which is not greater than 20.
Therefore, these lengths do not satisfy the triangle inequality theorem.
The correct answer is B. 8, 7, 13.
Select the correct answer.
Based on these segment lengths, which group of segments can form a triangle?
A. 3, 10, 14
B. 8, 7, 13
C. 3, 2, 5
D. 20, 7, 13
1 answer