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?
Aisha is correct in her reasoning. In congruent triangles, corresponding angles are equal, which means that corresponding angles with the same position in their respective triangles are equal. Therefore, ∠G≅∠C is a valid statement.
Sebastian's reasoning is incorrect because being on endpoints of their respective triangles does not necessarily mean that the angles are equal.
Conner's reasoning is also incorrect because being closest to the congruency sign does not necessarily mean that the angles are equal.
Bot is right :))
To determine which student is correct in their reasoning, let's analyze each statement:
1. Sebastian says ∠B≅∠F because they are both on endpoints of their respective triangles.
Sebastian's reasoning is incorrect. The fact that two angles are located at endpoints does not imply that they are congruent.
2. Aisha says ∠G≅∠C because both letters are in the middle of their respective triangles.
Aisha's reasoning is also incorrect. The placement of letters in the middle of each triangle does not guarantee that the corresponding angles are congruent.
3. Conner says ∠H≅∠P because both letters are closest to the congruency sign in their respective triangles.
Conner's reasoning is incorrect as well. The placement of letters relative to the congruency sign in each triangle does not determine their congruence.
Therefore, none of the students' reasoning is correct in this case.
To determine which student is correct in their reasoning, let's analyze each student's statement:
1. Sebastian says ∠B≅∠F because they are both on endpoints of their respective triangles.
Sebastian is correct in his reasoning. When comparing geometric figures, corresponding parts are the ones that are in the same position in each figure. In this case, ∠B and ∠F are both on endpoints of their respective triangles, so they are corresponding parts.
2. Aisha says ∠G≅∠C because both letters are in the middle of their respective triangles.
Aisha's reasoning is incorrect. Corresponding parts of congruent figures do not have to be in the same position in the figure. The fact that ∠G and ∠C are both in the middle of their respective triangles does not necessarily mean they are corresponding parts.
3. Conner says ∠H≅∠P because both letters are closest to the congruency sign in their respective triangles.
Conner's reasoning is also incorrect. The position of a letter next to the congruency sign does not determine whether two angles are corresponding parts or not.
Based on the analysis above, Sebastian is the student who is correct in their reasoning. ∠B≅∠F because they are both on endpoints of their respective triangles.