How to prove that one line …
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Posted by Swapnil Shinde 5 years, 3 months ago
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Sia ? 5 years, 3 months ago
Proof: Let us prove this statement by contradiction method. Let us assume that the line segment PT has two midpoints R and S.
{tex}\Rightarrow \quad P R=\frac{1}{2} P T{/tex}...........(1)
{tex}P S=\frac{1}{2} P T{/tex} .......... (2) ({tex}\because{/tex} R and S are mid-points according to assumption)
from (1) and (2) , we get
{tex}\Rightarrow{/tex} PR = PS
But this is possible only if R and S coincide. { which may not be possible if R and S are two different points }
Therefore,Our contradiction is incorrect.
i.e. there is only one mid-point of every line segment.
Hence, proved
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