# Transversals

A line which intersects two or more lines at distinct points are known as Transversals.

## Examples of Transversal line

Example 01
Transversal T intersecting two lines

In the above image you can observe;
L & M are the two non intersecting lines.
T is a transversal intersecting the lines M & N at points a & b

Example 02
Transversal T intersecting three lines

In the above figure you will observe;
L, M & N are three lines intersected by transversal T at three distinct points a, b & c

Example 03
Examples of Non-Transversal lines

In the above example, T is not a transversal because it intersects the lines M & N at the same point O.
To qualify as a transversal, the intersection should be at distinct points.

In the above example, T is not a transversal as it intersect only one line.
To qualify as transversal, it should intersect atleast two points.

Here we will discuss the angle formation when the transversal intersects two points

In the above figure, transversal intersects two line M & N at two distinct points.
Below are some angle properties:

(a) Interior Angles
Angles which lie inside the lines M & N are called Interior angles

Here angles 3, 4, 5 and 6 are the interior angles

(b) Exterior Angle
Angles which are located on the external sides of line M & N are called Exterior Angle

(c) Corresponding angles
Angles with the same matching corners with respect to transversal are called corresponding angles

Below are pairs of corresponding angles:
\angle 1\ and\ \angle 5
\angle 2\ and\ \angle 6
\angle 4\ and\ \angle 8
\angle 3\ and\ \angle 7

(d) Alternate Interior Angle
Alternate Interior angles are located between the two line and opposite side of the transversal

Below are alternate interior angle pairs
\angle 4\ and\ \angle 6
\angle 3\ and\ \angle 5

(e) Alternate Exterior Angle
These angles are positioned externally on the two line and placed opposite side of the transversal

Below are alternate exterior angle pairs
\angle 1\ and\ \angle 7
\angle 2\ and\ \angle 8

## Angle Property when transversal intersect parallel lines

When the two parallel lines M & N are intersected by transversal T, then following angle property is observed.

Corresponding Angles are equal
\angle 1\ =\ \angle 5
\angle 2\ =\ \angle 6
\angle 4\ =\ \angle 8
\angle 3\ =\ \angle 7

Alternate Interior Angles are equal
\angle 3\ =\ \angle 5
\angle 4\ =\ \angle 6

Alternate Exterior Angles are equal
\angle 1\ =\ \angle 7
\angle 2\ =\ \angle 8

Same Side Interior Angles are supplementary
\angle 4\ +\ \angle 5 = 180
\angle 3\ +\ \angle 6 = 180

## Questions on Transversals

(01) Is given line T transversal?

Solution
NO!!
As line T intersects M & N at common point O.

The transversal should intersect lines at distinct points.

(02) In the below figure, is line B transversal?

Solution

Yes, line B is a transversal as it intersects lines L, M & N at distinct points

(03) L & M are parallel lines and T is a transversal.
Study the figure below and find value of ∠a

Solution

Since L & M are parallel lines.
\angle b\ = \angle c\ {Corresponding Angles}
\angle b\ = 70 degree

Since L is a straight line, the sum of angles will be 180 degree
\angle b\ + \angle a\ = 180
70 + \angle b\ = 180
\angle a\ = 110 degree

(04) Two lines M & N are intersected by transversal T.
Find the alternate exterior angle of A

Solution

Alternate Exterior Angle is located at external side of the two lines and opposite end of the transversal

Here angle B is the alternate exterior angle pair of angle A

(05) In the below figure, L & M are two parallel lines intersected by transversal T
Find the value of angle B

Solution

\angle A\ = 106 degree

Angle A & B are same side interior angles.
When lines are parallel these angles are supplementary

\angle A\ + \angle B\ = 180
106 + \angle B\ = 180
\angle B\ = 180 – 106
\angle B\ = 74 degree