Answer :

i. Given, AB = BC …(i)


M is the mid-point of AB


AM = MB = …(ii)


and N is the mid-point of BC.


BN = NC = …(iii)


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


From Eq. (i), AB =BC


On multiplying both sides by ,


We get,



AM = NC [using Eq. (ii) and (iii)]


ii. Given, BM =BN …(i)


M is the mid-point of AB.


AM = BM = AB


2AM = 2BM = AB …(ii)


and N is the mid-point of BC.


BN = NC = BC


2BN = 2NC = BC …. (iii)


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


On multiplying both sides of Eq.(i) by 2,


We get, 2BM = 2BN


AB = BC [using Eq. (i) and (ii)]


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