Copy the figure

Copying a figure is a technique that works when two sides of a figure are congruent. In this case, we can copy the figure, or part of the figure, in order to continue making deductions. The most famous use of this technique is in the "three squares problem." In this case, each of the three squares are congruent, and thus, we're able to copy the figure, and after doing so, the solution falls out easily. Here's another problem where copying the figure is useful:

In this case, we copy just part of the figure, and we only do so after discovering all that we can about the subfigure. I have yet to see an instance of the technique of copying the figure be used multiple times in a single problem, although I imagine such a problem would look quite intimidating at first glance.