Write whether the following statement is True or False. Justify your answer.
The things which are double of the same thing are equal to one another.
The things which are double of the same thing are equal to one another.
(A) True.
This statement is one of Euclid's axioms. Euclid's axioms are fundamental assumptions used in geometry. Specifically,Euclid's sixth axiom states that "Things which are double of the same things are equal to one another."
If we have two quantities $x$ and $y$ such that both are double of a quantity $z$,then $x = 2z$ and $y = 2z$. Since both $x$ and $y$ are equal to $2z$,it follows that $x = y$.
This statement is one of Euclid's axioms. Euclid's axioms are fundamental assumptions used in geometry. Specifically,Euclid's sixth axiom states that "Things which are double of the same things are equal to one another."
If we have two quantities $x$ and $y$ such that both are double of a quantity $z$,then $x = 2z$ and $y = 2z$. Since both $x$ and $y$ are equal to $2z$,it follows that $x = y$.
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