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Question
In the following figure AB = BC, M is the mid-point of AB and N is the mid-point of BC. Show that AM = NC.
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Solution
Given, AB = BC ...(i)
M is the mid-point of AB.
∴ AM = MB = `1/2` AB ...(ii)
And N is the mid-point of BC.
∴ BN = NC = `1/2` BC ...(iii)
According to Euclid’s axiom, things which are halves of the same things are equal to one another.
From equation (i), AB = BC
On multiplying both sides by `1/2`, we get
`1/2` AB = `1/2` BC
⇒ AM = NC ...[Using equations (ii) and (iii)]
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