What is the reason for the fourth and eight steps in the proof?

Answer:
so the transitive property can be invoked in step 9
Step-by-step explanation:
Without the figure, it is difficult to tell what these steps do. However, the symmetry of the proof suggests that step 4 can match step 8, and its Reason can be "deduced from steps 2 and 3."
The idea of steps 4 and 8, taken together, is to show that DC and DB are both equal to DA, so the transitive property can be invoked in step 9.