In figure AB = BC ; BX=BY. Show that AX = CY ; State the Euclid's axiom used.

We have the diagram,

Given that, AB = BC …(i)

& BX = BY …(ii)

So, subtract the two equations (i) and (ii),

AB – BX = BC – BY

⇒ AX = CY

[Since, from the diagram we can observe that when BX is subtracted from AB, we are left with AX; Similarly, when BY is subtracted from BC, we are left with CY.]

Hence, shown.

This is the result of Euclid’s second axiom that states, if equals are subtracted from equals, then the remainder is also equal.