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(i) AB = BC, *m* is the mid point of AB and *n *is the mid point of BC. Show that AM = M C

(ii) BM = BN , M is the mid point of AB and N is the midpoint of *bc *show that AB = BC

(i) AB = BC,

*m*is the mid point of AB and

*n*is the mid point of BC. Show that AM = M C

(ii) BM = BN , M is the mid point of AB and N is the midpoint of

*bc*show that AB = BC

Please find below the solution to the asked query:

i ) Given : AB = BC, M is the mid point of AB and N is the mid point of BC.

From Euclid's 7

^{th}axiom we know " Things which are halves of same things are equal to one another . "

So,

$\frac{\mathrm{AB}}{2}=\frac{\mathrm{BC}}{2}$

**AM = NC ( Hence proved )**

ii ) Given : BM = BN, M is the mid point of AB and N is the mid point of BC.

From Euclid's 6

^{th}axiom we know " Things which are double of the same things are equal to one another . "

So,

2 BM = 2 BN

**AB = BC ( Hence proved )**

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