In geometry a line segment joining two nonconsecutive vertices of a polygon or polyhedron

is a kind of straight line. A diagonal line does not go straight up, down, or across. It is a line that connects two corners of a line

A diagonal line across a computer monitor

In mathematics, "diagonal" has different meanings. For example, in geometry a diagonal is any line that goes between the corners of a polygon. So a square has two diagonals, and a five-sided shape has five diagonals. In general the count of diagonal can be identified by a formula [n(n-3)]/2 where n is the total number of sides of shapes.

A diagonal connects 2 non-consecutive vertices of a convex polygon. It is not a word to be used to describe a slanted line. Lines in 2D are horizontal, vertical or oblique.