Parallel Lines and Transversals:

Parallel Lines:

Parallel lines are two-dimensional lines that do not meet or intersect. Intersecting lines are lines that have a common point.

Transversal Lines:

A line that meets or intersects two or more two-dimensional lines, each at a different point is called as a transversal line.

Transversal Postulate:

This is a special rule that states that if two parallel lines are intersected by a transversal, then the corresponding angles are congruent.

Alternate Angles:

Alternate angles are formed by a transversal line. These are angles lie on opposite sides of the transversal line. There are eight geometrical theorems concerning transversals. Some of them are stated as follows:

• If a transversal intersects 2 parallel lines, then the alternate interior angles are congruent.
• If a transversal intersects 2 parallel lines, then the corresponding angles are congruent.
• If a transversal intersects 2 parallel lines, then the alternate exterior angles are congruent.
• If a transversal intersects two lines such that the alternate exterior angles are congruent, then the lines are parallel.
• If a transversal intersects 2 parallel lines, then the interior angles on the same side of the transversal are supplementary.

Conditions to prove that lines are parallel:

There are four different ways to check if lines are parallel. They are stated as follows:

• The lines are said to be parallel, if they are cut by a transversal and the corresponding angles are congruent.
• The lines are said to be parallel, if they are cut by a transversal in such a way that the alternate interior angles are congruent.
• The lines are said to parallel, if they are cut by a transversal in such a manner that interior angles on the same side of the transversal are supplementary.
• The lines are parallel, if they are perpendicular and lie in the same plane.