Midpoints of the Sides of a Square

Proposed Problem 4 What is the figure formed by joining the midpoints of the adjacent sides of a square? Conjecture The figure formed by joinig the midpoints of the sides of a square 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 measurment of angles of the figure EFGH, which is formed by joining the midpoints of the adjacent sides of the square ABCD to check the correctness of the made conjecture.