Here, it is given terminal voltage is the closing side of the whole polygon. My question is how did this happen?
I can not understand the underlined lines.

 

If the voltages are represented by vectors then simple vector addition will explain how this works . If you do not understand vectors and the addition of vectors then I can not explain it to you, nor could others.

 

Instationous power is the product of the voltage times the current at that instant. In a single phase circuit
the voltage is a sine wave and (for a resistive load) the current is also and in sync. Thus the
power transfered varies over time:



With three phase the 3 separate pulses of power merge and from a constant flow of power.

 

Those three sine waves can also be represented by rotating vectors, which I think can make he explanation better. Once again, though, the TS needs to understand about vectors and how they can represent AC voltage and current.