Why does the Moon go through phases?

KEY

A: At New-Moon, the Moon as seen from the Earth is approximately in front of the Sun, therefore cannot be seen (unless it is exactly in front and causes a solar eclipse, in which case the Moon can be seen as a black shape obscuring the Sun).

B: At First Quarter the Moon is at right-angles to the Sun, therefore appears as a D-shape, with only the right-hand side lit-up.

C: At Full-Moon the Moon is approximately on the opposite side of the Earth to the Sun, therefore is fully lit-up (unless it is exactly opposite and causes a lunar eclipse, in which case it appears much darkened, usually reddish) .

D: At Three-Quarter Moon, the Moon is again only half-lit, this time on the opposite side seen from the Earth, therefore appears like a C-shape.