Easy
Solve the following question using an appropriate Euclid's axiom:
In the figure,we have $AB = BC$ and $BX = BY$. Show that $AX = CY$.
In the figure,we have $AB = BC$ and $BX = BY$. Show that $AX = CY$.
(N/A) We are given that:
$AB = BC$ ... $(1)$
$BX = BY$ ... $(2)$
According to Euclid's axiom $3$,if equals are subtracted from equals,the remainders are equal.
Subtracting equation $(2)$ from equation $(1)$,we get:
$AB - BX = BC - BY$
From the figure,$AB - BX = AX$ and $BC - BY = CY$.
Therefore,$AX = CY$.
$AB = BC$ ... $(1)$
$BX = BY$ ... $(2)$
According to Euclid's axiom $3$,if equals are subtracted from equals,the remainders are equal.
Subtracting equation $(2)$ from equation $(1)$,we get:
$AB - BX = BC - BY$
From the figure,$AB - BX = AX$ and $BC - BY = CY$.
Therefore,$AX = CY$.
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