State whether the following statement is true or false.

Two lines will be parallel to each other if they are parallel to the same line.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

It is given that two lines are parallel to the same line.
We know that the two lines will be parallel if the sum of the co-interior angles is

180 °,

and vice versa if the lines are parallel.
Question Image

Let’s assume that the lines l || m and l || n and t is a transversal.
Using the corresponding angles property, we have

∠ 1 = ∠ 2

and ∠ 2 = ∠ 3 ⇒ ∠ 1 = ∠ 3

Thus, if the transversal line t intersects three lines ‘l’ ‘m’, and ‘n’ such that l || m and l || n, then m || n.
Therefore, the two lines will be parallel to each other if they are parallel to the same line.
Thus, the given statement is true.
Hence, option (1) is correct.

Watch 3-min video & get full concept clarity