Question

Describe lengths of three segments that could not be used to form a triangle.

Segments with lengths of 10 in., 10 in., and ___ cannot make a triangle.
a 17
b 21
c 2
d 10

Answer 1

Segments with lengths of 10 inches, 10 inches, and 21 inches cannot form a triangle because they violate the Triangle Inequality Theorem, where the sum of two sides must be greater than the third side.

Step-by-step explanation:

To determine whether three line segments can form a triangle, we must consider the Triangle Inequality Theorem. This 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. Given two sides of equal length (10 inches each), the third side must be less than 20 inches for a triangle to be possible.

Possible third side lengths

• a 17 inches - Triangle Possible: 10 + 10 > 17
• b 21 inches - Triangle Not Possible: 10 + 10 is not greater than 21
• c 2 inches - Triangle Possible: 10 + 10 > 2
• d 10 inches - Triangle Possible: 10 + 10 > 10

Therefore, segments with lengths of 10 in., 10 in., and 21 in. cannot be used to form a triangle, as they do not satisfy the Triangle Inequality Theorem.