In the Fig.5.5, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC.


Given, X is the mid-point of AC


AX = CX=


2AX =2CX = AC …(i)


Y is the mid-point of BC.


BY = CY =


2BY = 2CY= BC …(ii)


Also, given AX=CY …(iii)


According to Euclid’s axiom, things which are double of the same things are equal to one another.


From Eq. (iii),


2AX = 2CY


AC=BC [from Eqs. (i) and (ii)]


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