seitwärts
sideways
In a direction to the side; from the center toward the left or right.
Er machte einen Schritt seitwärts, um Platz zu machen.
He took a step sideways to make room.

sideways
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sideways
In a direction to the side; from the center toward the left or right.
Er machte einen Schritt seitwärts, um Platz zu machen.
He took a step sideways to make room.

The word consists of 'Seite' (side) and the ending '-wärts' (-ward/-wards). This ending always expresses a direction, as also in 'vorwärts' (forward), 'rückwärts' (backward), or 'aufwärts' (upward).
Der Ball rollte langsam den Hügel abwärts.
The ball slowly rolled downward down the hill.
As an adverb, 'seitwärts' (sideways) describes the manner of a movement. It usually comes directly after the verb it modifies and answers the question 'Wie?' (How?) or 'Wohin?' (Where to?).
Die Krabbe bewegt sich seitwärts über den Sand.
The crab moves sideways across the sand.
'Seitwärts' (sideways) is almost always combined with verbs of movement or looking. Typical phrases are 'seitwärts gehen' (to walk sideways), 'seitwärts blicken' (to look sideways), 'einen Schritt seitwärts machen' (to take a step sideways), or 'seitwärts ausweichen' (to dodge sideways).
Er konnte dem Auto gerade noch seitwärts ausweichen.
He was just able to dodge sideways to avoid the car.
across / transverse
'quer' and 'seitwärts' both have to do with a direction to the side. 'seitwärts' describes movement to the left or right, especially from the point of view of a person or body. 'quer' more often describes a direction across something or against the lengthwise direction, for example 'quer über einen Platz' (across a square) or 'quer durch einen Raum' (across a room). They can be confused because both mean not forward. 'seitwärts' fits well with body movements; 'quer' is more common for paths, lines, or the position of things.

Meine Nachbarin geht seitwärts durch die enge Tür, weil sie eine große Kiste trägt.
My neighbor goes sideways through the narrow door because she is carrying a large box.
Aylin geht quer über den Parkplatz zum Eingang.
Aylin walks across the parking lot to the entrance.