# Transversal Line

What are Transversal Line?

The line which intersects two distinct lines in a plane at two distinct points is called a transversal.

In the below figure, line 't' is transversal to lines l and m, intersecting these two lines at points A and B.

Also, we observe in the below figure, line 't' is not transversal line because it intersects line l and m at one point only.

Angles made by the transversal with two lines:

l and m are two lines in a plane. Transversal 't' intersects these two lines at points A and B. Eight angles are formed, i.e., ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, ∠8. The angles marked have their special names.

Interior angles:

Angles whose arms include AB are called interior angles. In the given figure, ∠3, ∠4, ∠5, ∠6 are interior angles.

Exterior angles:

Angles whose arms do not include AB are called exterior angles. In the given figure ∠1, ∠2, ∠7, ∠8 are exterior angles.

Pair of corresponding angles:

These are pair of angles:

• Which lie on the same side of the transversal.

• If one is an interior angle, the other will be an exterior angle.

• They do not form a linear pair. In the figure, corresponding angles are: (∠2, ∠6); (∠3, ∠7); (∠1, ∠5); (∠4, ∠8)



Pair of alternate angles:

These are pairs of angles:

• Which lie on opposite sides of transversal.

• Both are either exterior angles or both are interior angles.

• They do not form a linear pair. In the given figure, alternate angles are:

(∠4, ∠6); (∠3, ∠5) these are interior alternate angles. In these pair of arms, arm AB is included.

(∠1, ∠7); (∠2, ∠8) these are exterior alternate angles. They do not include arm AB.

Pair of co-interior or conjoined or allied angles:

These are pairs of interior angles which lie on the same side on the transversal. In the given figure, co-interior angles are (∠3, ∠6); (∠4, ∠5)

Results when two parallel lines are cut by the transversal:

When parallel lines 'l' and 'in' are cut by the transversal line 't' then

• Pairs of corresponding angles are equal ∠2 = ∠6, ∠3 = ∠7, ∠1 = ∠5, ∠4 = ∠8

• Pairs of alternate angles are equal ∠4 = ∠6, ∠3 =∠5 , ∠ 1 = ∠7, ∠2 = ∠8

• Interior angles on the same side of transversal are supplementary ∠6 = 180°, ∠4 + ∠ 5 = 180°

Converse:

When two lines are cut by a transversal and if

• pairs of corresponding angles are equal

• or pairs of alternate angles are equal

• or interior angles on the same side of transversal are supplementary. Then two lines are said to be parallel to each other.

Lines and Angles

Fundamental Geometrical Concepts

Angles

Classification of Angles

Related Angles

Some Geometric Terms and Results

Complementary Angles

Supplementary Angles

Complementary and Supplementary Angles

Linear Pair of Angles

Vertically Opposite Angles

Parallel Lines

Transversal Line

Parallel and Transversal Lines