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. In other words, if a, b, and c are the lengths of the sides of a triangle, then the following conditions must hold true:

Question

a + b > c

a + c > b

b + c > a

Question:

1. True or False: The segments of lengths 5, 7, and 10 can form a triangle.

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2 points
True
False

Answer 1

1. True. According to 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. In this case, 5 + 7 = 12 which is greater than 10, 5 + 10 = 15 which is greater than 7, and 7 + 10 = 17 which is greater than 5. Therefore, the segments of lengths 5, 7, and 10 can form a triangle.

2. True. As explained in the previous answer, the segments of lengths 5, 7, and 10 can form a triangle. Therefore, the statement "True" is correct.