Trisection Points of the Sides of a Square

Proposed Problem 9

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




Hint

A Square is a quadrilateral with four equal sides and four right angles.

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