Tie for Two:
A & C are both regular figures
A & C have all angles congruent
A & C have all sides congruent
C & D are both quadrilaterals
B & D all the sides are different lengths
A & D have obtuse angles
B & D have acute angles
B & D are irregular figures

Thread for Three:
B, C, & D all have right angles
A, C, & D all have sets of parallel sides

Fit for Four:
They are all closed figures
They are all polygons
They are all convex