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Perpendicular lines intersect at a right angle, forming four 90-degree angles. This text explores their slopes, which are negative reciprocals, and how to calculate and formulate equations for lines perpendicular to a given line. Practical applications include building design and geometric problem-solving, demonstrating the importance of understanding these fundamental concepts in geometry.

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## Definition of Perpendicular Lines

### Essential concept in geometry

Perpendicular lines are two lines that intersect at a right angle, denoted by the symbol \( AB \perp CD \)

### Practical applications

Design of buildings

Perpendicular lines are used in the design of buildings, where walls intersect floors at right angles

Symbols

Perpendicular lines are also seen in various symbols, such as the cross on a first aid kit

### Relationship to slopes

The slopes of perpendicular lines are negative reciprocals of each other

## Slopes of Perpendicular Lines

### Definition of slope

The slope of a line quantifies its steepness and direction

### Relationship to perpendicular lines

The slopes of perpendicular lines are negative reciprocals of each other

### Calculation of slope

The slope of a line perpendicular to a given line can be found by taking the negative reciprocal of the given line's slope

## Equations of Perpendicular Lines

### Deriving the equation

The equation of a line perpendicular to a given line can be found by substituting the negative reciprocal of the given line's slope into the slope-intercept form

### Determining the y-intercept

The y-intercept of a perpendicular line can be found by using a known point through which the line must pass

### Practical examples

Perpendicular lines and their equations are useful in solving geometric problems, such as determining if two lines are perpendicular or finding the equation of a line passing through a specific point and perpendicular to a given line

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