It is given that 2(a+b)= x+y and x+y = 2c. Use the transitive property of equality: if a = b and a = c, b = c
x + y = 2c and x + y = 2(a +b)
=> 2c = 2(a +b)
divide both sides by 2
=> c = a + b
This proves that a + b = c
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