Question 87
Ali is given a piece of paper shaped like an equilateral triangle. He cuts the paper into two pieces with one cut. Then, he puts the pieces arbitrarily on a table and cuts them both with one cut to get four pieces of paper. Lastly, he puts all four pieces on the table and cuts them all with one cut to get eight pieces. In the end, he will have eight pieces of paper using three cuts.
Ali wants to do this in such a way that in the end, seven pieces are equal to each other but not to the last one.
a) Prove that if seven pieces are equal, then they are either triangles or quadrilaterals.
b) Prove that the seven equal pieces cannot be quadrilaterals.
c) Is it possible for the seven equal pieces to be triangles and not equal to the last one?
Ali wants to do this in such a way that in the end, seven pieces are equal to each other but not to the last one.
a) Prove that if seven pieces are equal, then they are either triangles or quadrilaterals.
b) Prove that the seven equal pieces cannot be quadrilaterals.
c) Is it possible for the seven equal pieces to be triangles and not equal to the last one?