teilen
to share
To use, own, or consume something together with one or more people.
Wollen wir uns die letzte Pizza teilen?
Should we share the last pizza?

to share / divide
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to share
To use, own, or consume something together with one or more people.
Wollen wir uns die letzte Pizza teilen?
Should we share the last pizza?

The verb 'teilen' is directly related to the noun 'der Teil' (the part, the portion). When you 'teilen' (share/divide) something, you make several parts out of it.
Kannst du den Kuchen in acht gleiche Teile schneiden?
Can you cut the cake into eight equal pieces?
The preposition after 'teilen' changes the meaning: you share something 'mit' (with) a person, you divide something 'in' (into) pieces or groups, and you divide a number 'durch' (by) another.
Er teilt sein Essen mit seinem Freund.
He shares his food with his friend.
When you share something with someone, the thing is in the accusative and the person with whom you share is in the dative after the preposition 'mit' (with). The structure is: subject + teilt + accusative object + mit + dative object.
Ich teile mir ein Zimmer mit meiner Schwester.
I share a room with my sister.
'Teilen' is also used for abstract things such as opinions, interests, or feelings. In this case, it means that you think or feel the same as another person.
Ich teile deine Begeisterung für dieses Projekt nicht.
I don't share your enthusiasm for this project.
In the context of the internet and social media, 'teilen' has a special meaning: to post content (e.g., a photo, an article, a video) on your own profile so that your friends or followers can see it.
Wenn dir der Beitrag gefällt, teile ihn bitte mit deinen Freunden.
If you like the post, please share it with your friends.
The reflexive verb 'sich teilen' means that something splits by itself into two or more directions or parts. It is often used for paths, rivers, or groups.
Hinter dem Hügel teilt sich der Wanderweg.
Behind the hill, the hiking trail splits.
to distribute / spread
'teilen' and 'verteilen' can both mean that something goes to several people or places. 'teilen' often emphasizes sharing something or making it into parts, for example 'einen Kuchen mit jemandem teilen' (to share a cake with someone). 'verteilen' emphasizes the action of giving something to several people or bringing it to different places. For example, you can 'Zettel in der Klasse verteilen' (hand out papers in class) or 'Creme auf der Haut verteilen' (spread cream on the skin). The words can be confused because when you distribute something, it is often divided first. If shared use is important, 'teilen' fits; if handing out or spreading out is important, 'verteilen' is a better fit.

Heute teilst du dir das Zimmer mit deinem Bruder.
Today you are sharing the room with your brother.
Sie verteilt morgen die Einladungskarten an alle Nachbarn.
Tomorrow she will hand out the invitation cards to all the neighbors.