proof that every line segment has a unique mid-point
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Let C and D be 2 mid point of line segment AB.
Since C is the mid point, AC = CB= 1/2 AB
Similarly AD = BD= 1/2 AB
Thus AC= AD
AD + CD= AD
therefore CD=0 units or C collides with D
hence every line segment has one and only one playground
:)
If C is the midpoint then AC = CB.
Again if D is the midpoint then AD = DB.
This is only possible if C and D coincides.
Thus line segment AB have a unique mid point.
hope it helps.