GoGeometry Action 153!

Creation of this resource was inspired by a tweet from Antonio Gutierrez (GoGeometry). Shown below are 4 SQUARES. You can move LARGE POINTS (3 vertices of the largest square and/or LARGE PINK POINT) anywhere you'd like.

What is the measure of the PINK ANGLE?

Interact here now. Here's some proof insight.

What geometry theorem is dynamically illustrated here (at the end)?

This illustration implies that the GREEN SQUARE (upper left) and PINK SQUARE (lower right) would fit PERFECTLY inside the BLUE SQUARE (middle). We saw this from the first GeoGebra applet above. How can we logically conclude this from the dynamics shown in the 2nd applet?

How can we formally prove what is dynamically illustrated here?

Quick (Silent) Demo