Show the Rectangle is Golden

A Golden Rectangle has the property that if the original rectangle is partitioned into a square and a new rectangle, the resulting rectangle is similar to the original rectangle. The question is: How does one check for similarity? Click [Rotate Rectangle] and [Check the Ratios] below and see.


This GoldenMean app was created in honor of John Golden (@mathhombre), who, in ten valuable minutes, taught me how to do animations with buttons in GeoGebra.