What are Parallel Lines?
Parallel lines are straight lines that never intersect or cross each other and are at a constant distance from each other. A few real world examples of parallel lines include railroad tracks where the two tracks run parallel to each other. Zebra crossings, a staircase are also a few other examples.
Geometrically, parallel lines are denoted by the symbol “∥”. The symbol “∥” implies ‘is parallel to’.
The image shows us two sets of parallel lines. Line ‘a’ is parallel to line ‘b’, and line ‘p’ is parallel to line ‘q’, and these parallel lines are represented as,
‘a∥b’ and ‘p∥q’.
Now let’s take a look at non-parallel lines. If two lines are not at a constant distance from each other or are intersecting at a point, then they are not considered to be parallel lines.
What are the properties of Parallel Lines?
Now that we know the definition of parallel lines, we can enlist a few of their properties:
- Parallel lines are a set of straight lines.
- Parallel lines do not intersect or cross each other.
- Parallel lines are always at the same distance from each other.
- Parallel lines are denoted by the symbol “∥”.
Solved Examples
Example 1: In the image can you identify the pair of lines that are parallel to each other.
Solution:
In the given image lines AC and DF are not intersecting and appear to be at the same distance from each other.
Hence, AC∥DF.
Similarly, we can say that HG∥BE.
Hence, the pairs of lines AC and DF, and HG and BE are parallel to each other in the image.
Example 2: Jacob says that line ‘A’ is parallel to line ‘B’ because they are not intersecting. Has Jacob made the right observation?
Solution:
The lines ‘A’ and ‘B’ are not intersecting but they do not appear to be at the same distance from each other. At the top, the distance between them is shorter than the distance between the two lines at the bottom of the image.
So, line ‘A’ is not parallel to line ‘B’.
Hence, Jacob has not made the right observation.
Example 3: Look at the image and identify the roads that are parallel to 2nd street.
Solution:
Observe the image and look for the road that does not intersect with 2nd street.
Only 3rd street does not cross 2nd street, and it appears to be at a constant distance from it.
Hence, 3rd street is parallel to 2nd street.
The real-life examples of parallel lines are the edges of sidewalks, rails of a ladder, rail tracks, the opposite sides of a ruler among many other examples.
Intersecting lines forming two to four right angles are known as perpendicular lines.
Lines that cross each other at exactly one point are called intersecting lines. Also two lines can intersect only at one distinct point.
Lines that are at a constant distance from each other and do not cross each other are called parallel lines. Hence, parallel lines do not intersect at any point.