Angle Bisector of a Right Triangle

Move point P.  What do you observe?

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

1. What can you say about the diagonal of the outer square in relation to its angles? in relation to the right triangles formed by the square? 
2. What can you say about the diagonal of the outer square in relation to the inner square?
3. What conjecture can you make from your observation in 2?

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