In the given figure, we have AB = BC, BX = BY, show that AX = CY, state the axiom used.

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Hi!
Here is the solution:

AB=BC
 

AX+BX = BY+CY
 

AX + BY = BY+CY ( because BX = BY)
 

Subtracting BY from both sides we get,
 

AX = CY
 

Hence Proved

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