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Question
In the following figure BM = BN, M is the mid-point of AB and N is the mid-point of BC. Show that AB = BC.
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Solution
Given, BM = BN ...(i)
M is the mid-point of AB.
∴ AM = BM = `1/2` AB
⇒ 2AM = 2BM = AB ...(ii)
And N is the mid-point of BC.
∴ BN = NC = `1/2` 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 equation (i) by 2, we get
2BM = 2BN
⇒ AB = BC ...[Using equations (ii) and (iii)]
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