Let's break down the statements made by Sebastian, Aisha, and Connor regarding the angle relationships implied by the statement \( BGH = PCF \).
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Sebastian's Statement: He says \( \angle B = \angle F \) because they are both at the endpoints of their respective triangles. This reasoning does not hold in general; being at the endpoints of triangles does not imply that the angles are equal without additional information about the triangles' congruency or properties. Therefore, Sebastian is not correct.
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Aisha's Statement: She claims \( \angle G = \angle C \) because both letters are in the middle of their respective triangles. Similar to Sebastian's reasoning, being in the middle of a triangle does not necessarily mean the angles are congruent. This also depends on the properties of the triangles. Thus, Aisha is also not correct.
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Connor's Statement: He states \( \angle H = \angle P \) because both letters are closest to the congruency sign in their respective triangles. This reasoning is more valid if the congruency statement \( BGH \cong PCF \) (which is implied by \( BGH = PCF \)) indicates that the two triangles are congruent, thus corresponding angles are congruent. Therefore, Connor’s reasoning is correct if \( BGH \) and \( PCF \) are indeed congruent triangles.
In summary, based on the correctness of the reasoning provided:
- Connor is the only student who is correct.