What is a Perpendicular Line?

Perpendicular lines are straight lines that intersect at a 90-degree angle – just like the two sides of a right triangle. In a plane, these lines can be represented using the Cartesian coordinate system, with a point of intersection at the origin. It is also possible to describe a line as perpendicular to another, given two points on one of the lines. The perpendicular line will then intersect the original line at the same point.

Perpendicular Lines in Geometry

In traditional Geometry, two lines that line intersect at a right angle are said to be perpendicular. Lines with a slope of zero (horizontal lines) and lines with an infinite slope (vertical lines) are also considered to be perpendicular. In this system, anything other than a right angle (90 degrees) is not considered a right angle, even though the angle might appear to be very close to a right angle.

Perpendicular Lines and Angles

In Math and more specifically in Trigonometry, the term ‘perpendicular’ refers to an angle that is between 0 and 90 degrees when measured in a counter-clockwise direction from the positive x-axis. It is considered to have an acute angle to its opposite angle, also known as the complementary angle. Two lines that intersect at an angle of 90 degrees are said to be at right angles to each other.

Two lines are said to be parallel if they do not intersect or touch each other at any point. To sum up, a perpendicular line is a line that intersects at a 90-degree angle from another line, forming a right angle. It is usually represented visually with a square shape. Consider the example of a square, each side of which intersects at a 90-degree angle with its other sides. These angles between the sides of the square together form four right angles.

In conclusion, we can say that a perpendicular line is one that intersects a line at a 90-degree angle. It is most often represented using a Cartesian coordinate system and has no slope – it is either a horizontal or vertical line. Additionally, two lines parallel to one another form a right angle. Finally, the term ‘perpendicular’ also applies to acute angles that are between 0 and 90 degrees – these angles form complementary angles with each other.