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.

Answer 1

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

a + b > c

5 + 7 > 10

12 > 10

This condition is true, so the segments can form a triangle.