Barry, Tony, and Denise are analyzing the statement triangle ABC ≅ triangle DEF(1 point) Responses Barry says < A ≅ < F because they are both on endpoints of the triangles Barry says < A ≅ < F because they are both on endpoints of the triangles Tony says < B ≅ < E because both letters are in the middle of the triangle congruence statement. Tony says < B ≅ < E because both letters are in the middle of the triangle congruence statement. Denise says < C ≅ < D because both letters are the closest to the congruence sign on the triangles

Answer 1

In the context of triangle congruence, the statements made by Barry, Tony, and Denise are correct, but let's analyze them for clarity:

1. Barry states that \( \angle A \cong \angle F \) because they are both endpoints of the triangles. This is incorrect in reasoning. The statement of triangle congruence doesn't imply endpoint relationships. Instead, it indicates corresponding parts, meaning \( \angle A \) corresponds to \( \angle F \) based on their position in the congruence statement.

2. Tony correctly states that \( \angle B \cong \angle E \) because both letters are in the middle of the triangle congruence statement. This is correct. In triangle ABC ≅ triangle DEF, the correspondence established is that the angles and sides correspond to one another based on their position in the congruence statement: \( A \) corresponds to \( F \), \( B \) corresponds to \( E \), and \( C \) corresponds to \( D \).

3. Denise states that \( \angle C \cong \angle D \) because both letters are closest to the congruence sign on the triangles. This is also correct. The positioning of the angles relative to the congruence statement confirms that \( \angle C \) corresponds to \( \angle D \).

In summary, the correct correspondence based on the statement \( \triangle ABC \cong \triangle DEF \) is:

• \( \angle A \cong \angle F \)
• \( \angle B \cong \angle E \)
• \( \angle C \cong \angle D \)

So while Tony and Denise are correct in their assertions, Barry's reasoning is flawed.