These are similar by SSS similarity. The corresponding sides are all in proportion to one another. For example, side AB is corresponding to side YZ, so the similarity ratios are
40/30 = 50/37.5
If you reduce both of those ratios down by division, you will get that both sides reduce down to 1 1/3. Therefore, they are similar by SSS similarity. Not congruency. Congruency is different.
Triangle STU is congruent to triangle UTX is the missing step. AAS (angle-angle-side) is a method of proving 2 triangles congruent, and using the already proved information, you can find the triangles that are congruent by AAS.
