Tilting Triangles

As the triangle rotates compare what part of the square is not covered by it anymore and what part of the square is newly covered.

Does the triangle continue to cover the whole of the portion of the square it moves over as its size reduces. What is special when the triangles side is of length $ \sqrt 2 $ units?

Is there a point where the whole of the triangle is always in the square and what effect does that have?