Definition of Parallel Lines.

Lines are an integral part of mathematics and contribute many exciting properties. Of all the types of lines, parallel lines are the most interesting to study.

Parallel lines are non-intersecting lines that do not cross each other at any place possible. They are always equidistant from one another and possess exciting properties as well. It is stated that parallel lines can meet at infinity.

Here we will discuss multiple aspects associated with parallel lines and parallel lines definition. Parallel lines possess extensive application in mathematics and physics calculations as well. 

What are the lines?

Lines can be described as groups of points that can be extended infinitely. Lines were first introduced for determining straight bodies devoid of any thickness or depth. Lines can be segregated into four types:

Horizontal lines: lines are moving from left to right in a straight direction are considered horizontal lines.

Vertical lines: lines that move up and down in similar straight lines are considered vertical.

Perpendicular lines: lines that intersect with each other at ninety degrees are considered perpendicular lines.

Parallel lines: lines that do not intersect at any point or meet at infinity are called parallel lines.

Definition of parallel lines.

According to the parallel lines definition, if two lines do not possess any common intersecting point and never cross their path throughout the journey, they are called parallel lines. The symbol which represents parallel lines is ‘||’.

For example, according to the definition of parallel lines, when we represent two lines, we write AB||CD. These parallel lines will run parallel to each other without intersecting.

Essential properties of parallel lines.

The distance between the parallel lines is always the same, so parallel lines are said to be equidistant, and they never cross each other’s path, nor do they meet at a certain point.

It is generally believed that parallel lines can meet at infinity.

Parallel lines are always straight lines.

The transitive property of parallel lines: lines that are seen to be parallel to the same line are also considered parallel. For example, if line C is parallel to line B, and line B is parallel to line D, then line C is parallel to line D. This is called the transitive property of parallel lines.

Symmetric characteristic of parallel lines: according to this property, two or more parallel lines are always symmetric. If line A is parallel to line B, then line B is also parallel to lie A.

Angles property of parallel lines:

• According to this property, the corresponding angles of parallel lines are equal.
• The vertically opposite angles are the same.
• The alternate interior angles are the same.
• The alternate exterior angles are also the same.

Theorems are related to parallel lines.

Theorem 1.

According to this theorem, if two parallel lines intersected by a transverse line, the pair of alternate interior angles are equal. The reverse of this theorem is also true. If the alternate interior angles are similar, then the lines present in the diagram are also parallel to each other.

Theorem 2.

According to this theorem, if two parallel lines intersect by a transverse line, then the pair of interior angles present on the same side of the transverse line are always supplementary. The reverse of this theorem is also true, which is that if the pair of interior angles are supplementary, then the lines present in the diagram will be parallel to each other.

Example:

AB and CD are considered to be parallel lines. EH is a transversal. Then what will be the measure of ∠AFG?

AB CD EH is considered to be the transversal.

So, FGD + ∠DGH = 1800_______ (angles here are in linear pair)

∠FGD = 180 – 119

∠FGD = 610

Now, ∠FGD = ∠GFA _____ (pair of alternate interior angles)

Therefore, ∠AFG = 610_____(since ∠FGD = 610).

Conclusion.

Understanding the integral aspects of parallel lines and parallel lines definition is essential for growing more profound knowledge in mathematics and physics. Here we have discussed multiple properties of parallel lines. You can study them along with parallel lines definition questions. 

Parallel lines definition questions and parallel lines definition previous year questions will help you out in understanding the pattern of questions and better knowledge about the topic. Make sure you go through the basics before solving parallel lines definition of previous year’s questions.