Given the congruence statement \(\triangle BGH \cong \triangle PCF\), we can conclude that corresponding angles and corresponding sides of the triangles are congruent. Based on the standard naming convention of congruence, we can match the angles as follows:
- \(\angle B\) corresponds to \(\angle P\)
- \(\angle G\) corresponds to \(\angle C\)
- \(\angle H\) corresponds to \(\angle F\)
Thus, the correct statements based on the congruence would be:
- \(\angle B\) is congruent to \(\angle P\)
- \(\angle G\) is congruent to \(\angle C\)
- \(\angle H\) is congruent to \(\angle F\)
Therefore, the correct conclusion would be: None of the listed options (\(\angle B \cong \angle F\), \(\angle G \cong \angle C\), \(\angle H \cong \angle P\)) is correct based on the matches.
To answer the original question, it would be best noted that: It is impossible to tell with the information given. (as the listed statements are not congruent based on the congruence provided).
However, if you're asked to choose the correct congruence relation that matches, none of those sets of angles listed have the correct correspondence according to the given triangles. If one of the options were \(\angle B\cong\angle P\), \(\angle G\cong\angle C\), or \(\angle H\cong\angle F\), that would be correct corresponding pairs.
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