I am struggling to solve the following problem:
divide parallelogram in three isosceles triangles. These triangles don't have to be equal. Provide all possible solutions and prove, that there are no other.
I have figured out couple of solutions, e.g. in case parallelogram is rectangle or square. Another one is when parallelogram has angles and . Then if we divide angle in three equal parts, then whole parallelogram also is divided in three isosceles triangles.
The problem is I can't figure out all solutions or a general one, and prove that there are no other solutions.
Really hope you can help me with that.
Thanks in advance!