Step 1: Let and be rhombuses. By the definition of a rhombus, . Step 2: Dilate rhombus by the scale factor given by . Side will be the same length as because of how I chose the scale factor. Because all sides of a rhombus are congruent, will be the same length as and therefore the same length as will be the same length as , and will be the same length as . That means all the corresponding sides of and will be the same length. Step 3: If all the sides in 2 figures are proportional, then those figures are similar, so there must be a sequence of transformations that take onto using dilations and rigid motions. Step 4: Translate by the directed line segment so that and coincide. Step 5: Rotate by angle so that and coincide. Now segments and coincide. Step 6: If needed, reflect over segment so that and are on the same side of . Now segments and coincide. Step 7: Once 3 vertices of the rhombus are lined up, the other vertex has to line up as well or else the shapes wouldn’t be rhombuses. So, we have shown we can use rigid motions and dilations to line up any 2 rhombuses, and therefore, all rhombuses are similar.