It is given that,

AC = BC

AC + AC + BC + AC (Equals are added on both sides) … (1)

Here, (BC + AC) coincides with AB. It is known that things which coincide with one another are equal to one another.

∴ BC + AC = AB … (2)

It is also known that things which are equal to the same thing are equal to one another. Therefore, from equations (1) and (2), we obtain AC + AC = AB

2AC = AB

∴ AC = 1/2AB