Let’s show that triangle $ABC$ is similar to triangle $DEF$:

Two figures are similar if one figure can be transformed into the other by a sequence of translations, rotations, reflections, and dilations. There are many correct sequences of transformations, but we only need to describe one to show that two figures are similar.

One way to get from triangle $ABC$ to triangle $DEF$ follows these steps:

• Reflect triangle $ABC$ across line $f$
• Rotate $90^\circ$ counterclockwise around $D$
• Dilate with center $D$ and scale factor 2

Another way to show that triangle $ABC$ is similar to triangle $DEF$ would be to dilate triangle $DEF$ by a scale factor of $\frac12$ with center of dilation at $D$, then translate $D$ to $A$, then rotate it $90^\circ$ clockwise around $D$, and finally reflect it across the vertical line containing $DF$ so it matches up with triangle $ABC$.