Angular Trisectors of an Isosceles Trapezium

Proposed Problem 7

What is the figure formed by joining the four intersection points of the adjacent angular trisectors of the interior angles of an Isosceles Trapezium?






Conjecture

The figure formed by joining the four intersection points of the adjacent angular trisectors of the interior angles of an isosceles trapezium is a quadrilateral kite.




Hint

A kite is a quadrilateral with two distinct pairs of equal adjacent sides.

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