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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