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.
True. The segments of lengths 5, 7, and 10 can form a triangle because they satisfy the conditions of the triangle inequality theorem:
5 + 7 > 10
5 + 10 > 7
7 + 10 > 5