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.
*
2 points
True
False
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.