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If A,B and C are three points on a line and B lies between A and C,then prove that AB+BC=AC

Given, A, B and C are three points on a line and B lies between A and C.

 

By the line segment addition axiom, we have

l(AB) + l(BC) = l(AC)

Thus, AB + BC = AC

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In the figure given above, AC coincides with AB + BC. Also, Euclid's Axiom (4) says that things which coincide with one another are equal to one another. So, it can be deduced that

AB + BC = AC

Note that in this solution, it has been assumed that there is a unique line passing through two points.

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AB=AC-BC
BC =AC-AB 
AB+BC=AB 
HENCE PROVED
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AB=AC-BC
BC =AC-AB 
Add above equation ( AB+BC)= 2AC -( AB+BC)
2(AB+BC) = 2 AC  Hence
AB+BC=AB 
HENCE PROVED
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