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The simple answer is that a rectangle IS NOT always a square. A square is always a rectangle, though, because it has 4 corner angles of 90 degrees, and opposite sides are parallel and equal in length.
The corner of a square or rectangle is 90 degrees.
A square and a rectangle are two of them.
A right-angle triangle is half of a square or rectangle. Draw a square or rectangle and draw a line from one corner to the corner diagonally opposite. You now have two triangles of the same area.
If a tile is a square or rectangle, cut the tile from corner to corner and you will create two triangles.