Your life is appaling.
The general term for the visible lit part of the moon is "the phase of the moon." The visible lit portion can have a crescent shape, a gibbous shape or a "half-moon" (half circle) shape.
Half
When the moon appears half lit, you are seeing exactly half of its surface. Half of the moon is illuminated by the sun, while the other half is in shadow. This phase is known as the first quarter when the moon is waxing, and the third quarter when the moon is waning.
The half of the moon that faces earth is in full sunlight.
"Waxing half" typically refers to the phase of the moon when it is transitioning from a new moon to a full moon, specifically when half of the moon's surface is illuminated. This phase is also known as the first quarter moon. During this time, the right half of the moon appears lit in the Northern Hemisphere, while the left half appears lit in the Southern Hemisphere. The term "waxing" indicates that the illuminated portion is increasing.
Beause there is only one sun in our solar system.
A week after the new Moon, when half of the Moon's face is illuminated, it is called the First Quarter phase. During this phase, the Moon appears as a semi-circle, with the right half lit up in the Northern Hemisphere. This occurs as the Moon moves in its orbit and more of its surface becomes visible from Earth.
This happens about once a month. We call this the "third quarter" phase of the moon.
When the moon is half lit on the left side, it is called the "Last Quarter Moon" or "Third Quarter Moon." This phase occurs when the moon has completed three-quarters of its orbit around the Earth, resulting in the left half being illuminated as viewed from Earth.
If the hemisphere that is 'lit' is facing away from the earth then it is a new moon
In a gibbous moon phase, most of the moon that we see is lit.
This is the first quarter phase. The moon looks half lit, half in shadow, but you actually can only see one quarter of the moons surface at this point (during a full moon, you would only be able to see half of the moons surface - the half that faces us).