Question & Answer

Two lines parallel to the same line are parallel to each other.

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Hint: Mathematics includes the study of topics which are related to quantity, structure , space and change. It has no generally accepted definition.

Complete step-by-step answer:
Mathematics is related to all the phenomena occurring in the world. When mathematical structures are good models of real phenomena mathematical reasoning can be used to provide insight or predictions about nature. One of the most important branches of mathematics is geometry. It includes the analysis of figures using simple theorems and results. According to our problem, we have to draw three lines in a geometrical plane which are parallel. So, this can be represented as:

In this figure, three lines AB, CD and PQ are drawn. From this figure, it is evident that AB is parallel to PQ and CD is parallel to PQ. Hence, both the lines AB and CD are parallel to one same line PQ. So, AB and CD are also parallel.
Therefore, we concluded that this statement is true.
Hence, option (a) is correct.

Note: This problem can be solved alternatively by just drawing the figure accurately and observing it carefully. On the basis of our observation, we can easily predict that both the lines are parallel. These observation skills will enhance the confidence of students.