Answer:
In \[\Delta ABM\], \[AB+BM>AM\] \[\left| \begin{align} & \text{Sum of the length of any two side of a triangle } \\ & \text{is greater than the lenth of the third side} \\ \end{align} \right.\] In \[\Delta ACM\], \[CA+CM>AM\] ? (2) \[\left| \begin{align} & \text{Sum of the lenths of any two sides of a triangle} \\ & \text{is greater than the lenth of the third side} \\ \end{align} \right.\] Sum (1) and (2), \[(AB+BM)+(CA+CM)>AM+AM\] \[\Rightarrow \] \[AB+(BM+CM)+CA>2AM\] \[\Rightarrow \] \[AB+BC+CA>2AM\]
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