Question

given: $overline{ad}perpoverline{af}$, $overline{fc}perpoverline{ch}$, $angle1$ and $angle2$ are vertical angles. prove: $angle dcongangle h$

Explanation:

Step1: Analyze the proof - structure

We need to justify step 6 which is the same as step 5.

Step2: Determine the reason

Since $\angle D\cong\angle H$ was already shown in step 5, the reason for step 6 (restating it) can be considered as referring back to the previous valid step. In a proof, when we restate a previously - established congruence, a common reason is 'Given' (in the sense of it being already given as true from a previous correct step in the proof).

Answer:

1. Given (as the statement $\angle D\cong\angle H$ is already established in step 5 and this is just restating it, and the most basic reason for restating what is already proven is 'Given' or in some proof - writing systems, just referring back to the previous step where it was established)