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 explain why or why not.
Measurements of each object:
pencil #1: 6 inches
pencil #2: 9 inches
pencil #3: 5 inches
Yes, we can make a triangle with these three objects because they satisfy the Triangle Inequality Theorem, which 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 this case, if we take pencil #1 and pencil #2 with lengths of 6 inches and 9 inches, their sum is 15 inches, which is greater than the length of pencil #3 (5 inches). Similarly, if we take pencil #1 and pencil #3 with lengths of 6 inches and 5 inches, their sum is 11 inches, which is greater than the length of pencil #2 (9 inches), and finally if we take pencil #2 and pencil #3 with lengths of 9 inches and 5 inches, their sum is 14 inches, which is also greater than the length of pencil #1 (6 inches).
Therefore, we can form a triangle using these three objects.