Two Squares and a Quadrilateral

A common vertex is shared by two squares A. Quadrilateral HIJK is formed using the segments joining the vertices and the midpoints of the diagonals of the square. What is the shape of the quadrilateral?

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Questions

1. Move the vertices of the two squares. Are your observations still the same? 
2. Make a conjecture about your observation. 
3. Prove your conjecture. 

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Reference
 http://www.ies.co.jp/math/java/geo/twosqsq/twosqsq.html