Jeremiah is working on a model bridge. he needs to create triangular components, and he plans to use toothpicks. he finds three toothpicks of lengths 4 in., 5 in., and 1 in. will he be able to create the triangular component with these toothpicks without modifying any of the lengths?

yes, according to the triangle inequality theorem
yes, according to the triangle sum theorem
no, according to the triangle inequality theorem
no, according to the triangle sum theorem

No, according to the Triangle Inequality Theorem

Step-by-step explanation:

The lengths of three toothpicks are 4 in., 5 in., and 1 in.

If they form a triangle the lengths of the sides of the triangle must satisfy the Triangle Inequality Theorem which states that the length of one side of a triangle must be less than the sum of the length of the other two sides of the triangle.

Now, we have 5 + 4 > 1 Hence, ok.

5 + 1 > 4 Hence, ok.

But, 4 + 1 = 5 Hence, not ok.

Therefore, the three toothpicks of lengths 4 in., 5 in., and 1 in. can not form a triangle as it does not follow Triangle Inequality Theorem. (Answer)