he 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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Answer 1

True: The sum of the lengths of any two sides is greater than the length of the third side for the segments of lengths 5, 7, and 10:

5 + 7 = 12 > 10

5 + 10 = 15 > 7

7 + 10 = 17 > 5