Sebastian, Aisha, and Conner are analyzing the

Question

statement ABGH = APCF.
Sebastian says <B = LF 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 LH = LP because both
letters are closest to the congruency sign in their respective triangles.
Which student is correct in their reasoning?
(1 point)None of the answers are correct.
• Conner
• Sebastian
• Aisha

Answer 1

To analyze the statement \( ABGH = APCF \), we need to identify what each student's reasoning is based on.

1. Sebastian's reasoning: \( \angle B = \angle F \) because they are both on endpoints of their respective triangles.

   • This reasoning is incorrect because simply being endpoints of triangles does not imply that the angles are congruent. The angles must be specifically corresponding angles based on the congruency of triangles.

2. Aisha's reasoning: \( \angle G = \angle C \) because both letters are in the middle of their respective triangles.

   • This statement seems plausible as it is referencing the included angles of the respective triangles when considering their correspondence. However, simply being "in the middle" is not sufficient to conclude congruence without knowing the specific triangles' arrangement.

3. Conner's reasoning: \( LH = LP \) because both letters are closest to the congruency sign in their respective triangles.

   • This reasoning is misleading. The proximity to the congruency sign does not guarantee that the sides or segments are equal unless they are specifically corresponding sides in congruent triangles.

Given the statements from all three students, none of the students provide a correct rationale for the assertions they made, as none of their reasons properly reflect the properties of congruent triangles. Therefore, the answer is:

None of the answers are correct.