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?
• None of the answers are correct.
• Conner
• Sebastian
• Aisha

Answer 1

To analyze the statement $ABGH=APCF$, we need to clarify the structure of the triangles or figures involved. The context suggests that $ABGH$ and $APCF$ are two geometric shapes that are said to be congruent.

1. Sebastian's reasoning: He claims that $\mathrm{\angle }B=\mathrm{\angle }F$ because they are at the endpoints of their respective triangles. This reasoning is flawed in the context because the position of angles at endpoints does not necessarily imply congruence without additional context about the triangles' properties.

2. Aisha's reasoning: She states $\mathrm{\angle }G=\mathrm{\angle }C$ because both letters are in the middle of their respective triangles. This is also not a valid reason to assert that the angles are congruent. The fact that the angles are in the middle does not guarantee that they are equal or that they correspond to one another in the context of the triangles or congruence.

3. Conner's reasoning: He contends that $LH=LP$ because both letters are closest to the congruency sign. Similar to previous points, proximity in notation does not imply congruence. Both segments $LH$ and $LP$ might or might not be congruent without further geometric reasoning or evidence.

Given these analyses, none of the students provided a correct reasoning for their claims regarding the triangles or statements concerning congruence. Therefore, the correct answer is:

• None of the answers are correct.