You're right!

During a full moon, the sunlit side
of the Moon faces the Earth.

FYI: Moonlight is sunlight that has reflected off the Moon's surface and into your eyes. If the Sun's light were to go out, there would be no moonlight.

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This phase of the moon is at first-quarter. The lit portion appears as as a half-circle to viewers on Earth.

The next time you look at the moon in the night sky, imagine that the Sun must be in the direction of the light source.

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This is a new moon.
During a new moon, the dark side
of the moon faces the Earth.

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This phase of the moon is at third-quarter. The lit portion appears as as a half-circle to viewers on Earth.

The next time you look at the moon in the night sky, imagine that the Sun must be in the direction of the light source.