A single act of showing, or a habit of proving.
J’ai montré covers the ordinary past: « je lui ai montré la maison ». As with donner, the pronoun lui already contains the à, so you never add the preposition back.
The imperfect appears for repeated showing or for describing what something used to demonstrate: « les résultats montraient une baisse » — the results showed a decline. That reporting use is very common in writing.
💡 Focus at this level: Past — what you showed
1. « Je lui ai montré » — no extra « à ».
2. Data “shows” things too. « L’étude montre que… »
3. Imperfect for ongoing evidence. « Les chiffres montraient… »
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