In figure, if AC = BD, then prove that AB = CD.

Given that,
AC = BD ....(i)

AC = AB + BC as point B lies between A and C ....ii)

BD = BC + CD as point C lies between B and D ....iii)

From equations (i), (ii) and (iii), we get,

AB + BC = BC + CD
\(\Rightarrow \) AB = CD.