Prove that every line segment has one and only one midpoint.
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Answer:
Step-by-step explanation:
Let us consider, a line segment AB.
Assume that it has two midpoints say C and D
Recall that the midpoint of a line segment divides it into two equal parts
That is AC = BC and AD = DB
Since C is midpoint of AB, we have A, C and B are collinear
AC + BC = AB ---------- (1)
Similarly, we get AD + DB = AB ------------ (2)
From (1) and (2), we get
AC + BC = AD + DB
2 AC = 2AD
AC = AD
This is a contradiction unless C and D coincide.
Therefore our assumption that a line segment AB has two midpoints is incorrect.
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