Question

Two lines parallel to the same line are ______ to each other.
A. Parallel
B. Non-parallel
C. Opposite
D. Perpendicular

Answer 1

Hint: We will actually assume a line X and draw a line ${{L}_{1}}$ parallel to X and again draw line ${{L}_{2}}$ parallel to X, then try to visualize the line segment ${{L}_{1}}$ and ${{L}_{2}}$ and then choose the correct option to fill the blank.

Complete step by step solution:
It is given in the question that two lines parallel to the same line then they are _____ to each other. We have to fill in the blank with the most appropriate word given in the option.
First of all what is a line segment? So, basically the line has no end points and it extends endlessly in both directions. The line which has no end point and it extends endlessly in both directions is called a line.

But the line segment has two endpoints. AB is a line and CD is a line segment in below figure.

 We can say that the shortest distance between any two fixed points is a line segment. Now, let us assume that we have a line X.

We have a line ${{L}_{1}}$ which is parallel to X

We also have a line ${{L}_{2}}$ which is parallel to X.

So, from diagram we can clearly say that ${{L}_{1}}\parallel X\parallel {{L}_{2}}$ therefore ${{L}_{1}}\parallel {{L}_{2}}$. It means the other two lines ${{L}_{1}}$ and ${{L}_{2}}$ are parallel to each other.
Also, we can say that if two lines are parallel to each other, they travel in the same direction. Therefore, we can say that if line 1 and line 2 have the same direction, and line 2 and line 3 have the same direction, therefore, it is understood that line 1 and line 3 also have the same direction.
Thus, the correct option is a) Parallel.

Note: Many times students read the question wrongly as two lines parallel to two lines instead of parallel to the same line. This may confuse them and they might choose the wrong option. Thus it is recommended to read the question carefully before solving it. If this question was asked for a single correct answer type question, then we could have tried eliminating options that mean the same, for example non-parallel and perpendicular mean the same, so we can avoid them. Now since direction of line is not given, opposite can also be avoided. Then we will get parallel as the answer.