Question

sebastian, aisha, and conner are analyzing the statement \\( \triangle bgh \cong \triangle pcf \\).
sebastian says \\( \angle b \cong \angle f \\) because they are both on endpoints of their respective triangles.
aisha says \\( \angle g \cong \angle c \\) because both letters are in the middle of their respective triangles.
conner says \\( \angle h \cong \angle p \\) because both letters are closest to the congruency sign in their respective triangles.
which student is correct in their reasoning?
(1 point)
sebastian
aisha
none of the answers are correct.
conner

Explanation:

When two triangles are congruent (\(\triangle BGH\cong\triangle PCF\)), the order of the letters in the congruence statement gives the correspondence of the vertices. So, \(B\) corresponds to \(P\), \(G\) corresponds to \(C\), and \(H\) corresponds to \(F\).

• Sebastian: \(\angle B\) corresponds to \(\angle P\) (not \(\angle F\)), so his reasoning is wrong.
• Aisha: \(\angle G\) corresponds to \(\angle C\) (because of the order in the congruence statement \(\triangle BGH\cong\triangle PCF\)), so her reasoning is correct.
• Conner: \(\angle H\) corresponds to \(\angle F\) (not \(\angle P\)), so his reasoning is wrong.

Answer:

Aisha