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 °