A half moon
Crazy
It is what ordinary people (not astronomers) usually call the "half Moon" phase. That describes it pretty well. We see exactly half of the Moon's Earth-facing side lit by the Sun. During first quarter the half that's illuminated is to the West.
The sun is perpendicular to the Earth and the Moon, in the direction of the bright half of the Moon.
When the right half of the moon is illuminated it would be called first quarter. (That's when you see the Moon from the northern hemisphere.)
Unless there is a lunar eclipse, half of the moon is always lit by the sun. Sometimes we see the lit half dead on (full moon), sometimes side on (half moon) and sometimes we don't see any of the lit surface (new moon) - usually we see something in between.
No. When you see the whole sun-lit side, you call it a "Full Moon".
First or Third Quarter
This is when you can only see half a moon out at night.
Half-moon Half-Earth
Sunlight is always falling on the moon and illuminating exactly half of it. That doesn't change.However, we're usually not in a place where we can see the entire lighted half of the moon.When we do happen to be in a position to see it all, that's when we call it a "Full Moon".
The moon is only visible because of the sun's light, which is why the moon appears to glow. When there is a half moon, only half of the moon is reflecting off the sun's light. It all has to do with the angle of the moon, the sun, and the Earth, which is why the moon has so many different phases.
Crazy
You often CAN see the "dark side of the Moon". It's easiest to do around the first quarter Moon or a day or two before that. The Sun shining on the Moon causes the Moon to reflect light, and we call this "moonlight". But if you were on the Moon and looking at the Earth, you could see the Earth by reflected sunlight, which we would call "earthlight". When we look at the first quarter Moon, we can often see the dark side of the Moon illuminated very slightly by reflected earthlight!
It is what ordinary people (not astronomers) usually call the "half Moon" phase. That describes it pretty well. We see exactly half of the Moon's Earth-facing side lit by the Sun. During first quarter the half that's illuminated is to the West.
We see the Moon from different angles. When the Moon is opposite to the Sun in the sky, we see the illuminated part. When the Moon is in front of the Sun, we see the dark part. At a 90 degree angle, we see half of the Moon illuminated, and half dark.
The sun is perpendicular to the Earth and the Moon, in the direction of the bright half of the Moon.
The Moon orbits the Earth, while the Earth is orbiting the Sun. Because the Moon is moving, we see it in different positions relative to the Sun; we call this the "phases of the Moon". Only when the Moon is on the opposite side of the Earth from the Sun will we see a "full" moon.