Dear expert please please tell me can i use axiom 3 in this question which is if equals are subtracted from equals , remainders are equal  (i)  in question 4 , point C is called a mid point of line segment of AB . prove that  every  line segment  has only one mid point

Dear Student,

Please find below the solution to the asked query:

Yes , You can use Euclid's third axiom to show a line can have only one mid point .

Let we have two mid points of line AB are C and D  , So

AC + BC  =  AB   and AD  + BD  =  AB ,  From first axiom " Things which are equal to the same thing are also equal to one another. " We get

AC + BC =  AD + BD    , Here BC  =  BD as C and D are point of AB )

From Euclid's third axiom "  If equals be subtracted from equals, the remainders are equal. "

We get

AC  =  AD 

Therefore,

A line can have only one mid point .

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