Find three objects (sticks, utensils, yarn, toys, books, etc.) that could represent the sides of a triangle. Can you make a triangle with these three objects? Use the triangle inequality theorem to explain why or why not.

Answer 1

Three objects that could represent the sides of a triangle are:

1. A stick that is 6 inches long
2. A stick that is 3 inches long
3. A stick that is 5 inches long

To determine if these sticks can form a triangle, we can use the triangle inequality theorem.

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, let's check if the sticks can form a triangle:

1. 6 + 3 = 9 < 5. This violates the triangle inequality theorem, as the sum of the lengths of two sides is not greater than the length of the third side. Thus, these sticks cannot form a triangle.