In geometry, a ** transversal ** is a line the intersects 2 or an ext other (often parallel ) lines.

In the figure below, line n is a transversal cut lines l and m .

once two or much more lines are cut by a transversal, the angles which occupy the exact same relative place are dubbed equivalent angles .

In the figure the bag of corresponding angles are:

∠ 1 and ∠ 5 ∠ 2 and ∠ 6 ∠ 3 and ∠ 7 ∠ 4 and ∠ 8

when the lines are parallel, the corresponding angles are congruent .

as soon as two present are reduced by a transversal, the bag of angle on one next of the transversal and also inside the two lines are called the consecutive internal angles .

In the above figure, the consecutive inner angles are:

∠ 3 and also ∠ 6 ∠ 4 and also ∠ 5

If two parallel lines are cut by a transversal, then the bag of consecutive interior angles developed are supplementary .

once two lines are reduced by a transversal, the bag of angle on either side of the transversal and also inside the 2 lines are called the alternate interior angle .

In the above figure, the alternate interior angle are:

∠ 3 and also ∠ 5 ∠ 4 and ∠ 6

If 2 parallel currently are cut by a transversal, climate the alternative interior angles formed are congruent .

when two lines are reduced by a transversal, the bag of angle on either side of the transversal and also outside the 2 lines are called the alternative exterior angles .

In the over figure, the alternate exterior angle are:

∠ 2 and ∠ 8 ∠ 1 and also ∠ 7

If two parallel currently are reduced by a transversal, climate the alternative exterior angles developed are congruent .

You are watching: If two lines are parallel to the same line, then they are _____ to each other.

** instance 1: **

In the over diagram, the lines j and also k are cut by the transversal l . The angles ∠ c and also ∠ e are…

A. Corresponding Angles

B. Consecutive internal Angles

C. Alternate Interior angles

D. Alternating Exterior angle

The angles ∠ c and also ∠ e lie on either side of the transversal together and also inside the two lines j and also k .

Therefore, they are alternate interior angles.

The correct selection is C .

** instance 2: **

In the over figure if lines A B ↔ and also C D ↔ room parallel and also m ∠ A X F = 140 ° then what is the measure of ∠ C Y E ?

The angles ∠ A X F and also ∠ C Y E lie on one side of the transversal E F ↔ and inside the 2 lines A B ↔ and C D ↔ . So, they are consecutive interior angles.

since the currently A B ↔ and also C D ↔ are parallel, by the consecutive interior angles to organize , ∠ A X F and also ∠ C Y E are supplementary.

the is, m ∠ A X F + m ∠ C Y E = 180 ° .

But, m ∠ A X F = 140 ° .

See more: How Many Bags Of Concrete Equal 1 Yard ? How Many Bags Of Concrete In A Yard

Substitute and also solve.

140 ° + m ∠ C Y E = 180 ° 140 ° + m ∠ C Y E − 140 ° = 180 ° − 140 ° m ∠ C Y E = 40 °