If 2(a+b)=x+y and x+y=2c,  then a+b=c. Is it true or false? Why?  

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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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