In a room with one light source, hold up a round object of some sort in front of you. Turn around. Note that half of the object is lit. But
* when you’re facing the light source, you don’t see that half;
* when you’re facing away, you see all the lit side;
* when you’re in between, you see part of the lit and part of the dark.
Who needs poorly drawn pictures? Wikipedia has good-quality pictures!
https://upload.wikimedia.org/wikipedia/commons/4/46/Moon_phases_en.jpg
The sun always lights up half the moon. Whatever fraction of the moon that we can see lit up, that’s because of the angle between us and the lit-up side. So if you see only a small crescent of lit-up moon, it’s because the moon is mostly between us and the sun, and we can only see a small fraction of the lit-up side. But a full moon is when the moon is behind us relative to the sun, so we can see the entire lit-up side.
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