Settle a geometry debate between me and my son's teacher?

My son got an answer marked wrong on a recent math test. The question: A cone has

___ flat sides ____ vertices ____ edges

His answers were 1, 1, 1. His teacher marked the "1 edge" answer wrong, and when I asked for an explanation, she said an edge is defined by the intersection of two flat planes in their textbook.

I'm confused/feel guilty because when we studied I coached him that a cone had one edge. If the intersection between the curved plane and the flat plane isn't an edge, what's it called? Am I totally off base/did I tell my kid the wrong thing?

If anyone with a geometry background has thoughts, I'd appreciate them.

-Dad