Query: If a point C lies between two points A and B such that AC = BC, then prove that AC \\(=\\frac{1}{2} \\mathrm{AB}\\). Explain by drawing the figure.
Context: It is given that,
AC = BC
Here, (BC + AC) coincides with AB. It is known that things which coincide with one another are equal to one another. 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
\\(\ herefore \\mathrm{AC}=\\frac{1}{2} \\mathrm{AB}\\)