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

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?

A. Aisha
B. None of the answers are correct
C. Sebastian
D. Conner

1 answer

To determine which student is correct in their reasoning about the congruence of the triangles △BGH and △PCF, we need to analyze what it means for two triangles to be congruent and how the corresponding angles relate to each other.

The notation \( △BGH ≅ △PCF \) indicates that triangle BGH is congruent to triangle PCF. This means that the corresponding angles and sides of the triangles are congruent.

  1. Sebastian's Claim:

    • He states that ∠B ≅ ∠F because they are on endpoints of their respective triangles. This reasoning is incorrect. The correspondence of angles is based on the congruence statement, not their positions in the triangle.
  2. Aisha's Claim:

    • She states that ∠G ≅ ∠C because they are both in the middle of their respective triangles. This reasoning does not correctly identify the corresponding angles based on the congruence statement. The angles in congruent triangles do not correspond solely based on their position within the triangles.
  3. Conner's Claim:

    • He states that ∠H ≅ ∠P because they are closest to the congruency sign in their respective triangles. While he is correctly identifying corresponding angles, he is incorrectly using positional reasoning rather than using the congruence statement to justify the correspondence of the angles.

Since none of the students correctly identified the corresponding angles based on the congruence statement, the correct answer is:

B. None of the answers are correct.

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