Definition
Diagonal
A diagonal joins two vertices of a shape that are not next to each other.
What it means
Choose a corner, skip the corners joined to it by sides or edges, and connect to another corner. That connection is a diagonal. A line is not a diagonal just because it looks slanted; the endpoints must be non-neighboring vertices of the shape.
Remember it
Skip a neighboring corner, then connect to a farther corner.
Example
A rectangle has four vertices. Joining the top-left vertex to the bottom-right vertex makes one diagonal; joining the other opposite pair makes the second diagonal.
Watch for
A side of a polygon is not a diagonal because its two vertices are adjacent.
Common mix-up
“Diagonal” names a connection between non-adjacent vertices, not any line drawn at a slant.
Exact meaning
A diagonal is a line segment joining two non-adjacent vertices of a polygon or polyhedron. In a polyhedron, it may lie across a face or pass through the solid, but it is not one of the solid’s edges.