Trisection Points of the Sides of a Quadrilateral

Proposed Problem 5

What is the figure formed by dividing the sides of a quadrilateral into three equal parts, and joining and extending adjacent points on either side of each vertex?



Conjecture

The figure formed by dividing the sides of a quadrilateral into three equal parts, and joining and extending adjacent points on either side of each vertex is a parallelogram.



Hint 1 | Hint 2

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

A parallelogram is a quadrilateral, in which each two opposite angles are equal in measure.

Please enable Java for an interactive construction (with Cinderella).
Drag free points A, B, C, or D to alter the quadrilateral ABCD and observe the length of each two opposite sides of the figure EFGH, which is formed by joining and extending adjacent trisection points on either side of each vertex of the quadrilateral ABCD, or the measurement of each two opposite angles of the same figure to check the correctness of the made conjecture.