Sebastian, Aisha, and Conner are analyzing the statement △BGH≅△PCF .

Question

Sebastian says ∠B≅∠F because they are both on endpoints of their respective triangles.

Aisha says ∠G≅∠C because both letters are in the middle of their respective triangles.

Conner says ∠H≅∠P because both letters are closest to the congruency sign in their respective triangles.

Which student is correct in their reasoning?

(1 point)
Responses

None of the answers are correct.
None of the answers are correct.

Conner
Conner

Sebastian
Sebastian

Aisha

Answer 1

In the statement \( \triangle BGH \cong \triangle PCF \), we know that the two triangles are congruent, which means that corresponding angles and sides of the triangles are congruent as well.

1. Sebastian claims \( \angle B \cong \angle F \) because they are at the endpoints of their respective triangles. This is incorrect; the angles that correspond to each other are determined by their positions in relation to the triangles, not merely because they are endpoints.

2. Aisha claims \( \angle G \cong \angle C \) because both letters are in the middle of their respective triangles. This is correct as \( \angle G \) from triangle \( \triangle BGH \) corresponds to \( \angle C \) from \( \triangle PCF \) based on their positions in the triangles.

3. Conner claims \( \angle H \cong \angle P \) because both letters are closest to the congruency sign in their respective triangles. This is correct as \( \angle H \) corresponds to \( \angle P \) based on the triangle congruence.

Based on this analysis, both Aisha and Conner are correct. However, since the prompt asks which singular student is correct in their reasoning and does not provide an option for both or a combined answer, it ultimately suggests that:

The best selection is Aisha, as she correctly identified the corresponding angles without ambiguity.

Final Answer: Aisha