Problem
Two rhombi make two shapes, not one: a straight pair and a bent pair.
A rhombus has two different corner angles, so the second tile can carry the line straight on or turn it. Each of the two has to be grown separately.
4.G.A.2Draw A DiagramAdd the third tile to every open edge of the straight pair and cross out turns and flips. Six survive.
The straight pair is the longer shape, so it offers more open edges that lead somewhere new: the row of three, and five in which the third tile turns a corner one way or the other.
4.G.A.2Make A Systematic ListGrowing the straight pair gives six shapes and growing the bent pair gives three, and since no shape appears on both lists the total is nine.
Every three-tile shape contains a two-tile shape, and there are only two of those, so growing each one in turn reaches every shape exactly once.
The two rhombi meet with no gaps or overlaps, so together they form one definite whole whose outline holds a fixed, countable set of open edges to try.
Any placement that is a turn or flip of one already on the list is not a new shape, so it is dropped.
Turning or flipping the arrangement lays it exactly onto the other one, keeping every side length and corner angle equal, so the two outlines are the very same shape.
The three arrangements that survive really are different, because none can be turned or flipped onto another.
When no turn or flip makes one outline lie exactly on another, some side or angle refuses to match, so the shapes are genuinely not the same.
The bent pair yields only three: a hexagon, a tent, a zigzag. Nothing is on both lists, so add.
None of those three can be built from the straight pair, so the two lists start apart and growing them never makes them meet.
4.G.A.2Count The ComplementTwo tiles already make two different shapes -- grow each one separately, then add the counts.