Angular Trisectors of a Parallelogram

Proposed Problem 3

What is the figure formed by joining the four intersection points of the adjacent angular trisectors of the interior angles of a parallelogram?






Conjecture

The figure formed by joining the four intersection points of the adjacent angular trisectors of the interior angles of a parallelogram is another parallelogram.




Hint

A parallelogram is a quadrilateral, in which each two opposite sides are equal in length.

 Please enable Java for an interactive construction (with Cinderella).
Drag free points A, B, or C to alter the parallelogram ABCD and observe the length of each two opposite sides of the figure EFGH, which is formed by joining the four intersection points of the adjacent angular trisectors of the interior angles of the parallelogram ABCD to check the correctness of the made conjecture.