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A slanted line or direction that connects two non-adjacent corners of a polygon, especially a quadrilateral.
Um die Fläche zu teilen, zog er eine diagonale Linie von einer Ecke zur anderen.
To divide the area, he drew a diagonal line from one corner to the other.
The context makes the meaning clear. In geometry or design, 'diagonal' describes a line between corners. In everyday language, it describes a slanted movement or arrangement in space.
Ein Rechteck hat zwei diagonale Linien gleicher Länge.
A rectangle has two diagonal lines of equal length.
In a geometric context, 'diagonal' is often used with verbs like 'ziehen' (to draw), 'verbinden' (to connect), or 'verlaufen' (to run) in combination with 'Linie' (line) or 'Achse' (axis).
Der Architekt zog eine diagonale Linie durch den Grundriss.
The architect drew a diagonal line through the floor plan.
'Diagonal' is very often used as an adverb to describe the manner of a movement. It then appears with verbs like 'laufen' (to walk/run), 'gehen' (to go/walk), 'fahren' (to drive), or 'schneiden' (to cut).
Schneide das Sandwich bitte diagonal durch.
Please cut the sandwich diagonally.
across / transverse
'quer' and 'diagonal' can both describe a direction that does not simply go straight ahead or lengthwise. 'quer' is more general and often means: from one side to the other or against the lengthwise direction. 'diagonal' is more precise when a line runs at an angle from one corner to the opposite corner, or diagonally across a surface. The words can be confused because a diagonal movement often also goes across something. If the slanted connection between corners is important, 'diagonal' fits better. If only the contrast with the lengthwise direction is important, 'quer' is enough.
Timo zeichnet eine diagonale Linie von der linken unteren Ecke zur rechten oberen Ecke.
Timo draws a diagonal line from the lower left corner to the upper right corner.
Der Hund läuft quer über die Straße.
The dog runs across the street.