Error Analysis A student says that in the below circle ∠RPO≅∠GPN

Question

since they are vertical angles, and thus RO≅NG
. Why is this incorrect?

Answer 1

This is incorrect because vertical angles are equal in measure, but they do not necessarily correspond to equal segments or sides in a circle. In a circle, angles are not directly comparable to each other in terms of lengths or segments. So, even if ∠RPO≅∠GPN, it does not imply that RO≅NG in a circle.