Defining Perpendicular Lines
Perpendicular lines are two or more lines that intersect each other at a right angle, which is exactly 90 degrees. This specific type of intersection creates four right angles at the point where the lines cross.
Section 2: The Symbol and Key Property
The key property of perpendicular lines is their 90-degree intersection. In mathematical notation, if line A is perpendicular to line B, it is written as A ⊥ B. The symbol '⊥' is used universally to denote perpendicularity. In coordinate geometry, the slopes of two perpendicular lines (that are not vertical or horizontal) are negative reciprocals of each other.
Section 3: A Real-World Example
A simple example of perpendicular lines can be found in the corners of a book or a square window pane. The horizontal edge and the vertical edge meet at a 90-degree angle, making them perpendicular to each other. Similarly, the x-axis and y-axis on a Cartesian coordinate plane are perpendicular lines.
Section 4: Importance in Geometry
The concept of perpendicularity is fundamental in geometry, engineering, and architecture. It is used to create stable structures, define grids and coordinate systems, construct geometric shapes like squares and rectangles, and solve problems involving distance and navigation.