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Transversal Lines

Transversal line is a straight line that cuts 2 or more lines. The lines may or may not be parallel. If the lines are parallel, then transversals tell us a great deal about the angles.

The transversal line makes angles equals to 900, if the lines are perpendicular.

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Transversal Lines Definition

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A line that crosses two or more lines in the same plane is known as transversal to those lines. Whenever a pair of lines are cut by a transversal, 8 angles are formed at the two points of intersection.

Transversal Line Definition

Transversal Lines and Angles

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A transversal is a line that passes through two lines in the same plane at different points. There are certain pairs of angles are created by lines and transversal with different vertices are given special names.

Angle Created by Transversal Line

Interior Angles: The angles which lie in between given lines.
In figure: $\angle$3, $\angle$ 4, $\angle$ 5 and $\angle$6 are interior angles since they lie in between lines a and b.

Exterior Angles: The angles which do not lie in between given lines.
In figure: $\angle$ 1, $\angle$ 2, $\angle$ 7 and $\angle$ 8 are the exterior angles since they do not lie in between lines a and b.

Alternate Interior Angles: Two angles formed by transversal with two lines are said to be alternate interior angles if
  • both the angles are interior angles
  • angles lie on the opposite sides of the transversal
  • angles do not form a linear pair.

In figure: $\angle$4 , $\angle$ 5 and $\angle$ 3, $\angle$ 6 are pairs of interior angles.

Alternate Exterior Angles: Two angles formed by a transversal with two lines are said to be alternate exterior angles if
  • both the angles are exterior angles
  • angles lie on opposite sides of the transversal
  • angles do not form a linear pair.

In figure: $\angle$1 , $\angle$ 8 and $\angle$ 2, $\angle$ 7 are pairs of exterior angles.

Corresponding Angles:

In figure: The pairs of corresponding angles are $\angle$ 1, $\angle$ 6; $\angle$ 4, $\angle$ 7; $\angle$ 2, $\angle$ 5; and $\angle$ 3, $\angle$ 8.

Co-interior Angles:

In figure: The pair of co-interior angles are $\angle$ 4, $\angle$6 and $\angle$ 3, $\angle$ 5.

Co-exterior Angles:

In figure: The pair of co-exterior angles are $\angle$ 1, $\angle$7 and $\angle$ 2, $\angle$ 8.

Transversal and Pairs of Lines

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Given below explains the transversal and pairs of lines.
Parallel Lines Cut by a Transversal Line

Transversal Line

In the above figure, AB and XY are parallel to each other and PQ is a transversal line.

There is a relation between the angles in M and N.

Non Parallel Lines Cut by a Transversal Line

Non Parallel Lines Cut by a Transversal

In the above figure, AB and XY are not parallel to each other and PQ is a transversal line.

There is no relation between angles in M and N.

Parallel Lines Cut by a Perpendicular Transversal Line

The perpendicular transversal is a transversal which is perpendicular to the parallel lines and makes all angles equal to 900 .

Parallel Lines with a Perpendicular Transversal

In the above figure, AB and XY are parallel to each other and PQ is a transversal line. All angles in M and N are equal to 900 .

Example Problems on Transversal Lines

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Given below are some of the example problems on transversal lines.

Solved Examples

Question 1:

Identify the missing angles in the following figure.

Transversal Lines Examples


Solution:

Given one of the angle of M is 450

From the figure, we can say AB is a straight line,

So, x 0 + 450 = 1800

Subtract 450 on both sides,

x 0 + 450 - 450 = 1800 - 450

x 0 = 1350 .

And, angle y0 is same as 450 (Vertical opposite angles)

The left out angle is same as angle x0 .

The angles of M are related to angles of N.

So, the resultant figure is

Parallel Lines Transversal



Question 2:

Identify the specified angle from the following figure:

Traversal Not in Parallel Lines


Solution:

In the given figure there are no parallel lines.

Given the angle b is 60o.

We know that the angle of a straight line is 1800.

So, a0 + b0 = 1800

a0 + 600 = 1800

Subtract 600 on both sides

a0 = 1200.

=> $\angle$ AMN = 60o and $\angle$ BMN = 120o. (Vertical opposite angles)

Traversal Not in Parallel Lines Examples

Since there is no relation between these two lines, thus we cant find the rest of the angles.



More topics in Transversal Lines
Transversal Line Properties Transversal Lines and Angles
Parallel Lines Cut by a Transversal
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