Lines

 

A line is defined as the one-dimensional object that can be extended in both directions. 
A line is of infinite length. 

Pairs of lines can relate to each other in four different ways namely:  

1) Intersecting Lines

Intersecting lines are lines that meet at a point. When two lines intersect, they define angles at the point of intersection.

2) Parallel Lines

Parallel lines are lines that never intersect. The distance between the two lines is fixed and the two lines are going in the same direction.

3) Perpendicular Lines

Perpendicular lines are lines that intersect at one point and form a 90° angle.

The following diagrams show the Intersecting Lines, Parallel Lines and Perpendicular Lines. Scroll down the page for more examples and solutions.

4) Pair of Intersecting Lines

When two lines intersect or cross each other, they are known as a pair of intersecting lines. For an intersection to occur, at least two lines are needed. Two intersecting lines necessarily have just one and only one common point.  The point where the two lines intersect or meet is known as intersecting point or the point of intersection. 

In the following image, a pair of intersecting lines is shown. Here, AB and CD are two intersecting lines which cross or intersect each other at the point O.

pair of intersecting lines form four angles at the point of intersection. In the above image, ∠∠1, ∠∠2, ∠∠3, ∠∠4  are those four angles. The angles that are opposite to each other are called vertically opposite angles. These angles are equal to each other.

In above diagram, ∠∠1, ∠∠3 and ∠∠2, ∠∠4 are vertically opposite angles. Thus, by the definition:

∠∠1 = ∠∠3

∠∠2 = ∠∠4

5) Pair of Parallel Lines

Two or more lines that never meet one another are known as parallel lines. We may define a pair of parallel lines as two lines that do not intersect at any point even if they are extended in either direction to the infinite length. 

The parallel lines are situated at the same distance from each other; i.e. distance between any two corresponding points on the lines is fixed.

A pair of parallel lines is shown in the following figure:

There are various angles that are formed when two parallel lines are cut by another line known as transversal (a line that is not parallel to them). The concepts related to angles play a vital role in geometry.

Let us suppose that AB and CD be two parallel lines and PQ be a transversal passing through them. The angles formed by these lines are demonstrated in the diagram given below: