Question

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

Answer 1

Answer:

your answer is in above picture

Answer 2

Answer:

Let A, B, and C be three distinct points of a line, with the respective coordinates x, y, and z. If x < y < z, then A-B-C.

Proof, By the ruler postulate:

AB= ly- xl

BC= lz - yl

AC= lx - xl

But y-x is positive because x < y; similarly, z-y and z-x are positive. So:

AB = y-x

BC = z-y

AC = z-x

Finally:

AB + BC = (y - x) + (z - y)

= z-x

=AC.

Since AB + BC = AC, A-B-C by the definition of between.If A, B and C are three points on a line, and B lies between A and C.