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: 7 inches
pencil #2: 6 inches
pencil #3: 8 inches
The three objects that could represent the sides of a triangle are pencil #1 (7 inches), pencil #2 (6 inches), and pencil #3 (8 inches).
To determine if a triangle can be formed with these three pencils, we need to check if the sum of the lengths of any two sides is greater than the length of the third side.
Let's check:
- 7 + 6 = 13 (greater than 8)
- 7 + 8 = 15 (greater than 6)
- 6 + 8 = 14 (greater than 7)
Based on the Triangle Inequality Theorem, since the sum of the lengths of any two sides is greater than the length of the third side for all combinations, a triangle can be formed with these three pencils.