From the above figure we get that,

AC = AB + BC

BD = BC + CD

And it is given is that AC = BD

So, AB + BC = BC + CD ………….(i)

According to Euclid’s axiom, when equals are subtracted from equals, the remainders are also equal.

Subtracting BC from both side in eq(i), we get

AB + BC − BC = BC + CD − BC

AB = CD