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5.In question 4, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.
Answer :

Here, C is the mid-point of line segment AB, such that AC = BC.
Let us assume that there are two mid-points C and C' of same line AB.
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Then as already proved, AC = 1/2 AB and also, AC' = 1/2 AB
Therefore, we get, AC = AC' ,which is only possible when C and C’ Coincide.
Hence, it is proved that every line segment has one and only one mid-point.