Ruben has two congruent wooden dowels. He cuts one dowel in two in order to have three pieces to make a triangle. Explain why, despite having three sides, Ruben will not be able to make a triangle with his three pieces.

Answer:

According to the Triangle Inequality Theorem, the sum of any two side lengths of a triangle must be greater than the length of the third side. Because Ruben cut one dowel into two pieces, the sum of those two pieces is equal to the length of the uncut dowel. Since the sum is not greater than the third side, a triangle cannot be formed.