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Solve the following question using the appropriate Euclid's axiom:
In the figure,we have $BX = \frac{1}{2} AB$,$BY = \frac{1}{2} BC$ and $AB = BC$.
Show that $BX = BY$.
In the figure,we have $BX = \frac{1}{2} AB$,$BY = \frac{1}{2} BC$ and $AB = BC$.
Show that $BX = BY$.
(N/A) We have $AB = BC$ [Given].
According to Euclid's axiom,things which are halves of the same things are equal to one another.
Since $AB = BC$,their halves must also be equal:
$\frac{1}{2} AB = \frac{1}{2} BC$.
Given that $BX = \frac{1}{2} AB$ and $BY = \frac{1}{2} BC$,we can substitute these into the equation above.
Therefore,$BX = BY$.
According to Euclid's axiom,things which are halves of the same things are equal to one another.
Since $AB = BC$,their halves must also be equal:
$\frac{1}{2} AB = \frac{1}{2} BC$.
Given that $BX = \frac{1}{2} AB$ and $BY = \frac{1}{2} BC$,we can substitute these into the equation above.
Therefore,$BX = BY$.
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