Angular Trisectors of a Rectangle

Proposed Problem 5

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







Conjecture

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




Hint

A rhombus is a quadrilateral with four equal sides.

Please enable Java for an interactive construction (with Cinderella).
Drag free elements (free points A and B, or semi free point C) to alter the rectangle ABCD and observe the length of 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 rectangle ABCD to check the correctness of the made conjecture.