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State true or false.

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

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Ture

False

answer is A.

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Detailed Solution

Suppose that there are three lines.
Line AB, Line CD and Line EF
Question Image

Now, in the given figure line AB is parallel to CD.
AB||CD
Also, the line EF is parallel to AB
AB||EF
Now, by the corresponding angles axioms,

∠ 1 = ∠ 2

and

∠ 1 = ∠ 3

Now angle 2 and 3 are corresponding. Thus, they are same in measure. Thus,

∠ 2 = ∠ 3

Now, by converse of corresponding angle axioms,
CD||EF
Thus, two lines which are parallel to same lines, in real they both are also parallel to each other.
So, given statement is true.
Hence, option 1 is correct.

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