Definition
Vertex
A point where geometric sides, edges, or rays meet.
What it means
A vertex is the exact meeting location often called a corner. In a polygon, follow two neighbouring sides until they meet; that point is a vertex. The plural of vertex is vertices.
Remember it
A vertex is a meeting point; vertices are meeting points.
Example
A triangle has three vertices because its three pairs of neighbouring sides meet at three points.
Watch for
A marked point halfway along a side is not a vertex, and a circle has no vertices because its boundary does not form corners.
Common mix-up
A vertex is a point; a side or edge is the segment that meets another one there.
Exact meaning
A geometric vertex is a point where sides of a polygon, edges of a solid, or rays of an angle meet. In a polygon, exactly two sides meet at each vertex.