Bilateral and Unilateral Descent
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Bilateral descent traces kinship through both parents equally; unilateral descent traces it through one parent's line only, whether patrilineal (father's line) or matrilineal (mother's line).
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A U.S. child's surname commonly follows the father's line even though inheritance and kinship are otherwise traced bilaterally.
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A society's descent rule and its power structure are related but not identical; a matrilineal society is rarely matriarchal.