Angular Trisectors of a Rhombus

Proposed Problem 4

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






Conjecture

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





Hint

A rectangle is a quadrilateral with four right angles.

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