In the figure,we have: $AC = XD$,$C$ is the mid-point of $AB$ and $D$ is the mid-point of $XY$. Using Euclid's axiom,show that $AB = XY$.

(N/A) Given that $C$ is the mid-point of $AB$,therefore $AB = 2AC$.
Given that $D$ is the mid-point of $XY$,therefore $XY = 2XD$.
We are also given that $AC = XD$.
Since things which are double of the same things are equal to one another (Euclid's Axiom),we can conclude that $AB = XY$.