Write how this apples the Triangle Inequality Theorem:

Question

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. So, for our example lengths, we need to check if the following conditions hold true:

Book + Pencil > Straw

→ (True)
Book + Straw > Pencil

→ (True)
Pencil + Straw > Book

→ (True)
Conclusion:
Since all three conditions of the Triangle Inequality Theorem are satisfied, you can indeed make a triangle with the chosen lengths of the books, pencils, and straws. If you follow these steps, you should be able to form a triangle using those common household objects!

Write the application of Triangle Inequality theorem in 5 sentences

Answer 1

The Triangle Inequality Theorem is a fundamental concept in geometry that helps us determine whether three given lengths can form a triangle. Specifically, it states that the sum of the lengths of any two sides must always be greater than the length of the third side. To apply this theorem, we can use everyday objects, such as a book, a pencil, and a straw, and assign them as the lengths we want to test. By checking the three conditions—Book + Pencil > Straw, Book + Straw > Pencil, and Pencil + Straw > Book—we can verify if these lengths satisfy the theorem. If all conditions hold true, we can confidently conclude that it is possible to construct a triangle with the chosen lengths.