As the name "angle angle" suggests, we need 2 pairs of angles proven congruent in order to prove that two triangles are similar. Each "angle" refers to a pair of angles between the two triangles, which are corresponding angles. We could use the third pair, but it's extra unnecessary work. This theorem is often written as "AA similarity" or something along those lines.
One way to check for similar triangles is to compare the ratios of the sides. If the corresponding sides divide to the same value, then you have similar triangles. This method only works of course if you know the side lengths.
