Q. 16

# In the Fig,(i) AB = BC, M is the mid-point of AB and N is the mid- point of BC. Show that AM = NC.(ii) BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that AB = BC.

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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