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

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

Answer 1

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

Using the inequality conditions:

5 + 7 > 10 (12 > 10) - True

5 + 10 > 7 (15 > 7) - True

7 + 10 > 5 (17 > 5) - True

Since all three conditions are true, the segments can form a triangle.

2. 2 points