3. I have recieved the information at this very moment. 4. It started raining without any warning5.Ram and Laxman left at the same time
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Answer:
I have received the information at this very moment.
Ram and Laxman left at the same time.
It started raining without any warning.
Explanation:
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Answer:
Let, AB be the line segment
Assume that points P and Q are the two different mid points of AB.
Now,
∴ P and Q are midpoints of AB.
Therefore,
AP = PB and AQ = QB.
also,
PB+AP = AB (as it coincides with line segment AB)
Similarly, QB+AQ = AB.
Now,
Adding AP to the L.H.S and R.H.S of the equation AP = PB
We get, AP+AP = PB+AP (If equals are added to equals, the wholes are equal.)
⇒ 2AP = AB — (i)
Similarly,
2 AQ = AB — (ii)
From (i) and (ii), Since R.H.S are same, we equate the L.H.S
2 AP = 2 AQ (Things which are equal to the same thing are equal to one another.)
⇒ AP = AQ (Things which are double of the same things are equal to one another.)
Thus, we conclude that P and Q are the same points.
This contradicts our assumption that P and Q are two different mid points of AB.
Thus, it is proved that every line segment has one and only one mid-point.
Hence Proved.
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