Transversal Lines

Transversal Line is a straight line that cuts 2 or more lines. The 2 or more lines may or may not be parallel. There is a relation with the angles formed by those lines, if the lines are parallel. If the lines are not parallel, there is no relation. The transversal line makes angles equals to 90⁰, if the lines are perpendicular.

Parallel Lines Cut by a Transversal Line

Parallel Lines Cut by a Transversal" title="Two Parallel Lines Cut by a Transversal" width="300" />

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

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 .

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 90^{0 .}

Below are example problems on transversal lines

Example 1 - Identify the missing angles in the following figure.

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 = 135^{0 .}

Since the given lines AB and PQ are parallel the given angle is equal to y⁰

So angle y⁰ is same as 45⁰

The left out angle is same as angle x⁰ .

The angles of M are related to angles of N.

So the resultant figure is

Example 2- Identify the specified angle from the following figure:

Solution:

In the given figure there are no parallel lines.

Given the angle b is 160^o.

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

So a⁰+b⁰= 180⁰

a⁰+160⁰ = 180⁰

Subtract 160⁰ on both sides

a⁰= 20⁰.