To determine which option the artist did not use to show proportion in the image, let's consider how proportions are commonly established in facial drawings:
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Lining the corners of the mouth up with the center of the eyes - This is a common proportion used in facial sketches.
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Lining up the sides of the nose with the inside corners of the eyes - This is also a common proportional guideline.
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Lining up the bottom of the mouth with the tops of the ears - This is not a standard proportional guideline; typically, the bottom of the chin lines up more closely with the ears, but not specifically the bottom of the mouth.
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Lining up the inside edge of the eyebrows with the inside corner of the eyes - This is a recognized proportion in facial drawing.
Given this reasoning, the artist did not use the option related to "lining up the bottom of the mouth with the tops of the ears" as a method to show proportion in the image.