Transversal Lines

A straignt line that cuts two or more line which are in the same plane is called as transversal line.

TransversalLine

In the above figure: we can see line 1, 2 and 3 are co-planar lines.{lines in the same plane} They are cut by another line t. So, t is called as transversal line.

Alternate Angles and corresponding angles created by transversal lines

There are different angles called as alternate and corresponding angles that are created by transversal line with the lines that are transversed{or cut}.

Alternate angles:

When two lines are cut by a transversal, the pair of angles that are on alternate sides of the transversal line at two different points of intersection and inside the lines being cut are called "alternate interior angles ".

If the lines that are being transversed are parallel then alternate angles are equal.

AlternateInteriorAngles

In the above figure, we can see that

If the lines 1 and 2 are parallel then we  have  

When two lines are cut by a transversal, the pair of angles that are on alternate sides of the transversal line at two different points of intersection and outside the lines being cut are called "Alternate exterior angles".

AlternateExteriorAngles

In the above figure, we can see that
Is line 1 and line 2 are parallel then
Corresponding angles:

Corresponding angles are the angles that are on the same side of transversal line and at same or corresponding location at different intersection points of transversel and lines being transversed.

In the below figure,
CorrespondingAngles

If the lines that are being transversed are parallel, the corresponding angles are equal.

If line 1 is parallel to line 2,

Theorems relates to transversal lines

Below are the list of theorems related to transversal line:

Theorem 1 If a transversal intersects two parallel lines, then the alternate interior angles are congruent.

Theorem 2 If a transversal intersects two parallel lines, then the corresponding angles are congruent.

Theorem 3 If a transversal intersects two parallel lines, then the alternate exterior angles are congruent.

Theorem 4 If a transversal intersects two parallel lines, then the interior angles on the same side of the transversal are supplementary.

The next four theorems are converses of the above four theorems.

Theorem 5 If a transversal intersects two lines so that alternate interior angles are congruent, then the lines are parallel.

Theorem 6 If a transversal intersects two lines so that corresponding angles are congruent, then the lines are parallel.

Theorem 7 If a transversal intersects two lines so that alternate exterior angles are congruent, then the lines are parallel.

Theorem 8 If a transversal intersects two lines so that interior angles on the same side of the transversal are supplementary, then the lines are parallel.