Here are the correct definitions for each term, highlighted accordingly:
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Cast Shadow: the area that is the darkest right underneath an object, which gets lighter as it goes further away from the light source.
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Core Shadow: the area of an object in shadow that is the darkest.
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Reflected Light: light which is bounced back onto an object from the surface it sits on.
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Light Area: the area of a form that reflects the most light and is the lightest value in a drawing.
Feel free to ask if you need further clarifications!