to insure / to assure
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to insure
To conclude a contract with an insurance company in order to protect oneself against financial losses from a specific risk, such as an accident, theft, or illness.
Man sollte sein Auto unbedingt gegen Diebstahl versichern.
You should definitely insure your car against theft.
'Versichern' (to insure/to assure) is an inseparable verb derived from the adjective 'sicher' (safe/secure/sure). The prefix 'ver-' turns it into a verb with the basic meaning 'to make something secure.'
Bitte sichere die Leiter, bevor du hinaufsteigst.
Please secure the ladder before you climb up.
The grammar reveals the meaning: the preposition 'gegen' (against) points to insurance (m01). A dative object indicates that you are assuring someone of something (m02). The reflexive pronoun 'sich' means that you are checking something (m03).
Ich habe mein Fahrrad gegen Diebstahl versichert.
I insured my bicycle against theft.
When taking out insurance, you use the structure 'etwas versichern gegen' (to insure something against) + accusative. The accusative after 'gegen' names the risk.
Es ist ratsam, eine Reisegepäckversicherung gegen Verlust abzuschließen.
It is advisable to take out travel baggage insurance against loss.
To assure someone of something, the verb needs a person in the dative. The information being assured can follow as an accusative object or as a subordinate clause with 'dass' (that).
Der Arzt versicherte dem Patienten eine schnelle Besserung.
The doctor assured the patient of a quick recovery.
to claim / assert
'behaupten' and 'versichern' can both be used when someone says that something is true. However, 'behaupten' often sounds more neutral, or even somewhat doubtful: the other person says something, but it is not necessarily proven. 'versichern' is stronger and more personal. It is used when someone says emphatically that something is true or will happen, often to calm worries. The words can be confused because both make a statement about truth. The difference is: someone who 'behauptet' something presents it as true; someone who 'versichert' something wants to create trust.
Der Arzt versichert der Patientin, dass die Untersuchung nicht gefährlich ist.
The doctor assures the patient that the examination is not dangerous.
Am Abend behauptet ihr, dass niemand die Tür offen gelassen hat.
In the evening, you claim that no one left the door open.