All nouns in te reo Māori belong on one of two categories, known as the a and o categories. The possessive that is used will change depending on the category.
For example, food is the a category and so a person would say:
tāku kai
my food
But a house is in the o category, and so a person would say:
tōku whare
my house

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The woman is sleeping at the man's house
things in the 'o' category: where you live

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Rangi's bed is big
O category: your body and things associated with it, such as a bed

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Our tomato is red
All the singular personal possessives in the a and o categories

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My tummy is sore
All the possessive pronouns in the o category

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I love my boss
The o category for superiors

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Everything in the o category