If a point C lies between two points A and B such that AC = BC, then prove that AC = \(\frac{1}{2}\) AB. Explain by drawing the figure.
Solution and Explanation
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 = \(\frac{1}{2}\) AB
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