Question

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 1

idk if you can read the pic but basically if the half-dowels are each joined to one end of the long dowel (which they would have to be to make a triangle) as soon you rotate them away from the long dowel to make two sides they separate. to be a triangle, all sides have to connect - so no triangle

Answer 2

Triangles has the following rule:

a + b > c

where c is the length of the bigger side and a and b is the length of the other sides. If you form a triangle from two congruent wooden dowels, then you will have that the sum of the length of the two lesser sider is equal to the longer sides, violating the rule established before. Therefore, a triangle cannot be formed with the 3 pieces.