Easy
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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Solve the following question using an appropriate Euclid's axiom:
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In the figure,we have $AB = BC$ and $BX = BY$. Show that $AX = CY$.
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View SolutionRead the following two statements which are taken as axioms:
$(i)$ If two lines intersect each other,then the vertically opposite angles are not equal.
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$(i)$ If two lines intersect each other,then the vertically opposite angles are not equal.
$(ii)$ If a ray stands on a line,then the sum of two adjacent angles so formed is equal to $180^{\circ}$.
Is this system of axioms consistent? Justify your answer.
Easy
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