kreuzen
to cross
To intersect or cross, usually referring to lines, paths, or roads.
An der nächsten Ampel kreuzen sich eine Hauptstraße und eine Nebenstraße.
At the next traffic light, a main road and a side street cross.

to cross
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to cross
To intersect or cross, usually referring to lines, paths, or roads.
An der nächsten Ampel kreuzen sich eine Hauptstraße und eine Nebenstraße.
At the next traffic light, a main road and a side street cross.

The verb 'kreuzen' (to cross) is derived from the noun 'das Kreuz' (the cross). Many meanings have to do with the shape of a cross (+), that is, with something that intersects or overlaps.
Zeichne ein Kreuz auf das Papier.
Draw a cross on the paper.
The verb is often used reflexively as 'sich kreuzen' (to cross / to intersect). This describes two or more things (e.g., roads, glances, paths) meeting or overlapping at one point.
Unsere Blicke kreuzten sich für einen kurzen Moment.
Our eyes met for a brief moment.
The expression 'jemandes Wege kreuzen sich' (someone's paths cross) is very common. It means that people meet by chance, often after a long time.
Ich hätte nie gedacht, dass sich unsere Wege noch einmal kreuzen würden.
I would never have thought that our paths would cross again.
To describe a body posture, the past participle 'gekreuzt' (crossed) is often used like an adjective. The most common phrases are 'mit gekreuzten Armen' (with crossed arms) or 'mit gekreuzten Beinen' (with crossed legs).
Er saß mit gekreuzten Beinen auf dem Boden und meditierte.
He sat on the floor with his legs crossed and meditated.
In the biological meaning of breeding, the verb follows the pattern 'A mit B kreuzen' (to cross A with B). Here, A is one species and B is the other.
Man versuchte, einen Apfel mit einer Birne zu kreuzen.
They tried to cross an apple with a pear.
In the meaning 'to sail against the wind', 'kreuzen' (to tack) is a technical term from sailing. In this context, it is usually used without an object.
Der Kapitän entschied, vor der Küste zu kreuzen, um auf besseren Wind zu warten.
The captain decided to tack off the coast to wait for better wind.
to cross
'überqueren' and 'kreuzen' can both have to do with paths or lines that go across something else. 'Überqueren' usually describes a person or vehicle going or driving from one side to the other. 'Kreuzen' more often describes paths, roads, or lines intersecting. People's paths in life can also 'sich kreuzen' when they meet. Learners may confuse the words because both are sometimes connected to 'crossing'. If someone is actively going to the other side, 'überqueren' fits better; if two paths intersect, 'kreuzen' fits better.

Im Park kreuzen sich zwei Wege direkt vor dem kleinen See.
In the park, two paths cross right in front of the small lake.
Herr Hoffmann überquerte den Platz, um zur Bushaltestelle zu kommen.
Mr. Hoffmann crossed the square to get to the bus stop.