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:

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.

True
False

Answer 1

False

Explanation: Applying the triangle inequality theorem:

5 + 7 > 10 (True)
5 + 10 > 7 (True)
7 + 10 > 5 (True)

Since all three conditions are true, the segments of lengths 5, 7, and 10 can form a triangle.