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.

**Angles made by transversal**

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