In the given figure, (i) If AB=BC, then M is the midpoint of AB and N is the the midpoint of BC. Show that AM=NC. (ii) If BM = BN, then M is the midpoint of AB and n is the midpoint of BC. Show that AB = BC.

Dear Student,

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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