Ethan created three triangles: triangle x, triangle y, and triangle z. if mc003-1.jpg and mc003-2.jpg, which must also be true? the triangles are equilateral. the triangles are right triangles. triangles x and z are congruent. triangles x, y, and z share one or more vertices.

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.