Q. 144.2( 6 Votes )

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

Answer :

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.


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