Question

If A1 B1 and C are three points on a line and B lies between A and C, then prove that AB + BC = AC​

Answer 1

It seems to me there was printing mistake in question.

The question would be, If A,B,C are three points on a line and B lies between A and C. then prove that AB + BC = AC​..

considering the above question , we can say that:-

 AC is the complete line  and B is point on it.

we can see here that, AC is divided into two different parts including AB and BC.

 and AC=AB+BC.

hence proved that AB+BC=AC

Answer 2

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

To prove : AB + BC = AC

proof : according to given data, we have drawn it. and the diagram is shown in figure.

here it is clearly shown that line (AB + BC) coincides with line AC, don't it ?

now according Euclid's Axiom, Things which coincide with one another are equal to one another.

here (AB + BC) coincide with AC.

it means, AB + BC is definitely equal to AC.

⇒AB + BC = AC

[hence proved]