Given Information: 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:
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
1. False: In order for the segments of lengths 5, 7, and 10 to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. However, in this case, 5 + 7 is equal to 12 which is not greater than 10. Therefore, the segments of lengths 5, 7, and 10 cannot form a triangle.
2. False: The segments of lengths 5, 7, and 10 cannot form a triangle.