Children often resemble or behave like their parents.
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Children often turn out a lot like their parents.
When you say the apple doesn't fall far from the tree, you are pointing out how alike they are.
It can be a compliment or a criticism.
"Like Father, Like Son"
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A child behaves like their father, specific to father and son only
"A Chip off the Old Block"
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A person is very similar to their parent, usually said as a compliment
"The Apple Doesn't Fall Far from the Tree"
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A child's character or behavior reflects their parent's