Parallel and Perpendicular Lines – Explanation

Parallel Lines

Two lines going in a straight path, never intersecting or touching each other, are parallel lines.

Take the below figure, for example, where we have two lines, “a” and “b,” which, as shown, never meet each other.

                                                                                       Image is taken from splashlearn


Properties of parallel lines are as follows:

  • Parallel lines are straight lines.
  • Parallel lines have equal distances from each other.
  • Parallel lines never meet each other.
  • Parallel lines can be extended in any direction.


A transversal is a line that intersects two parallel lines.

When it does, many angles are formed, some of them are equal, and others are supplementary.

In the below figure, L1 and L2 are intersected by a transversal, and eight different angles are formed:


                                                                                                  Image is taken from splashlearn

  • Corresponding angles: Angles that are equal in measure; in the figure above, we can see there are four pairs of corresponding angles which are given below

∠a = ∠e, ∠b = ∠f, ∠c = ∠g, and ∠d = ∠h

  • Alternative Interior Angles: Angles are formed inside of two parallel lines and are equal in measure. These angles are given below

∠c = ∠e, ∠d = ∠f

  • Alternative Exterior Angles: Angles that are formed on either side of the transversal and in measurement, are equal

∠a = ∠g, ∠b = ∠h

  • Consecutive Interior Angles: Supplementary angles which are formed inside of transversal

∠c + ∠f = 180°, and ∠d + ∠e = 180°

  • Vertically Opposite Angles: When two lines are equal in measure and intersect each other

∠a = ∠c, ∠b = ∠d, ∠e = ∠g, ∠f = ∠h

Identifying Parallel Lines

Here are some of the characteristics which can help identify parallel lines

  • If the Corresponding Angles of two lines are equal.
  • If the Alternative Interior Angles of two lines are equal.
  • If the Alternative Exterior Angles of two lines are equal.
  • If the Consecutive Interior Angles on both sides of the transversal are supplementary.

Parallel Line Equation

Straight Line equation  y = mx + b

 where “m” is the slope and “b” is the y-intercept, “m” tells us how steep the line is by determining the slope.

Parallel Lines Symbol

Two Parallel Lines are denoted by putting “| |” between the two lines AB and CD as

AB | | CD

Perpendicular Lines

When two lines meet each other at an angle of 90 degrees, they are perpendicular lines.

                                                                                                                        Image is taken from cuemath

As given in the figure, there are two lines, AB and CD, intersecting at an angle of 90 degrees.


Perpendicular lines always intersect each other, but all are not perpendicular to each other; if it makes “L” shaped, the angle is a right angle, so the lines are perpendicular.

Some of the properties of perpendicular lines are as follows:

  • Perpendicular lines always intersect or meet each other at a right angle.
  • Perpendicular lines always make an angle of 90 degrees.
  • Two lines which do not cross each other cannot be perpendicular; they are parallel.

ldl4DO5GmAvUcYDTmk8ds45Twapqr5YD Hb1zNy5 he Cns8RXMDfHPxmdouC534IIIBUrLu 47bPwQZnbgbc7IaQJdN8UEB71DtT71ZPoccZg9 iqzJu1Su 83ITdJC A5mrr

                                                              Image is taken from splashlearn

  • Two lines which intersect each other at acute angles are not perpendicular.

fRzOzjdj3UldC6ukY4Ckb BuaQ0XRgS7FOJzy Yeskq2pjAAzmAS109ZQQryWYaiu7i8YB biOaE

                                                                Image is taken from splashlearn

  • Any line which is not intersecting at right angles is not perpendicular.

0q14 f1KyfWgyrohto1xiq5mkIbj6D0mVruI olXhd1A5IU3Ibhalq5CY1ldSkrVPOvoZ2ZBbz1GYnSz5dxVqtBTb2fMEilH9 ucL1j 4abgWIWNbdjIddqXTgTlUhi2Vzv69HMR

                                                              Image is taken from splashlearn


Some of the standard mathematical shapes have perpendicular lines:

  • Square
  • Right-Angled Triangle
  • Rectangle


In the given figure, the lines AB and CD are perpendicular (⊥) to each other.

If the given BOC angle is equal to 90 degrees, find the value of x

B1328KYJgyR3RRLdIzGklURa8FnywXbxz1ijsfo4EsvkuiLCuz1m onEXNmwLlap8Mds G9yG0dC41SO1kvr0GfD0JSrj lhQoQLww2zuh3

                                                                                                                    Image is taken from cuemath


First things first, a right-angled triangle can be made or given in any x,y plane; don’t be alarmed if you see it upside down.

BOC = 90°

x + 63° = 90°

x = 90° – 63°

x = 27°

Where x is 27°, if we add both 27° and 63°, we will get an angle of 90° which suggests that the lines are perpendicular to each other.

To Tech Times

TO TECH TIMES is going to become the ultimate technology platform, bridging the gap of Industry & Investor linkage with the grass-root level market. Building a Technology Hub where thousands of people going connect from the region where they can join, learn and reach the heights of success.

Leave a Reply

Your email address will not be published. Required fields are marked *

Back to top button