Perpendicular Lines

Perpendicular lines around us:

Have you observed the Red Cross sign keenly or the squares of a Rubik’s cube or the alphabet T of English language? One thing in common about these citations is that they illustrate perpendicularity of lines and surfaces. Let us discuss what perpendicular lines exactly are?

Perpendicular Lines

Now, what does perpendicularity exactly mean? We know that if a ray is rotated about its end-point, the measure of its rotation is called angle between its initial and final position.The value of any angle is proportional to its amount of rotation and the sense of its rotation. Clearly, greater the amount of rotation, larger will be the angle formed. A special case of angles is a right angle, in which the measure of rotation of a ray is 90o. When two lines or surfaces intersect to form right angles then such lines or surfaces are said to be perpendicular to each other.

Consider the following two line segments \(\overline{AB}\) and \(\overline{CD}\)  . These line segments are perpendicular to each other as they intersect at 90o at point X. Thus, both the line segments have a common intersection point i.e. X and are right angles to each other.

Perpendicular Lines

Perpendicular lines lie in the same plane i.e. they are co-planar and intersect at right angles.  Thus it implies that if you have two lines which are perpendicular to each other, then these lines will be at right angles and vice versa.

Using just a compass one can draw a perpendicular to a line. These straightedge techniques was developed by ancient Greeks. In case of co-ordinate geometry, a line is said to be perpendicular only if the slope of a line have a definite relationship.

If you simply look around you will find numerous examples of perpendicular lines and surfaces. The corners of the wall intersect each other at right angles, the tiles in the kitchen or the washroom, the intersection of roads at squares, hands of a clock when it strikes exactly three’ O clock,  the corners of your desk or the doors are examples illustrating perpendicularity.

To understand other concepts related to perpendicular lines and their properties, please download BYJU’S-The Learning App and boost your problem solving skills.

Practise This Question

Perpendicular lines make right angle (90°) with each other.