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Question
If a point C lies between two points A and B such that AC = BC, then prove that AC = `1/2` AB. Explain by drawing the figure.
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Solution
It is given that,
AC = BC
AC + AC = BC + AC ...(Equals are added on both sides) …(1)
Here, (BC + AC) coincides with AB. It is known that things which coincide with one another are equal to one another.
∴ BC + AC = AB …(2)
It is also known that things which are equal to the same thing are equal to one another. Therefore, from equations (1) and (2), we obtain
AC + AC = AB
2AC = AB
∴ AC = `1/2AB`
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