A figure can be transformed more than once. If a figure is transformed using only congruence transformations, then the preimage and image will be congruent. If a figure is transformed using a combination of congruence transformations and similarity transformations, then the preimage and image will be similar.
Let's try it! Determine the transformations that map figure 1 to figure 3.
To get from figure 1 to figure 2, the figure was rotated To get from figure 2 to figure 3, the figure was reflected across a vertical line.
So, to map figure 1 to figure 3, figure 1 was rotated and then reflected. Since rotations and reflections are both congruence transformations, figure 1 and figure 3 are congruent.
Let's try another example! Determine the transformations that map figure 1 to figure 3.
To get from figure 1 to figure 2, the figure was translated up and right.
To get from figure 2 to figure 3, the figure was dilated.
So, to map figure 1 to figure 3, figure 1 was translated and then dilated. Since translations are congruence transformations and dilations are similarity transformations, figure 1 and figure 3 are similar.
