Find three objects sticks, yarn, and books that could represent the sides of a triangle. Can you make a triangle with these objects? Could you use the Triangle Inequality Theorem to explain why or why not?
Then: Measurements of each object:
Application of Triangle Inequality Theorem:
Yes, sticks, yarn, and books could represent the sides of a triangle. You could use two sticks as two sides of the triangle, yarn as the third side, and books to prop up the sticks and yarn to form a triangle.
Measurements:
- Stick: 10 inches
- Yarn: 12 inches
- Book: 6 inches
To determine if a triangle can be formed with these objects, we can apply 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:
- Stick + Yarn = 10 + 12 = 22 inches
- Stick + Book = 10 + 6 = 16 inches
- Yarn + Book = 12 + 6 = 18 inches
Since 22 is greater than 10, 16 is greater than 6, and 18 is greater than 12, a triangle can be formed with these objects according to the Triangle Inequality Theorem.