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since that's true, then RO = RN - ON by straight algebraic subtraction of the same quantity from both sides of the equation.
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by the definition of betweenness, point O is between points R and N because of the following qualities:
1. R, O, and N are collinear.
2. segments RO + ON = RN
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by algebraic subtraction of equal quanitites from both sides of an equation, you have:
RO + ON = RN
subtract ON from both sides of the equation to get
RO = RN - ON
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