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Question

Draw any line segment, say $$\overline {AB}$$. Take any point $$C$$ lying in between $$A$$ and $$B$$ Measure the lengths of $$AB, BC$$ and $$Ac$$. Is $$AB = AC + CB$$?
[Note : It $$A, B, C$$ are any three points on a line such that $$AC + CB = AB$$, then we can be sure that $$C$$ lies between $$A$$ and $$B$$].


Solution

[Note: If A, B, C are any three points on a line such that AC$$+$$CB$$=$$AB, then we can be sure that C lies between A and B]
Answer:
It is given that point C is lying somewhere in between A and B. Therefore, all these points are lying on the same line segment $$\overline{AB}$$. Hence, for every situation in which point C is lying in between A and B, it may be said that AB$$=$$AC$$+$$CB.
For example,
$$\overline{AB}$$ is a line segment of $$6$$cm and C is a point between A and B, such that it is $$2$$cm away from point B. We can find that the measure of line segment $$\overline{AC}$$ comes to $$4$$cm.
Hence, relation AB$$=$$AC$$+$$CB is verified.

Mathematics
NCERT
Standard VI

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