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Perpendicular Lines

Master the properties and relationships of perpendicular lines in geometry

⊥What are Perpendicular Lines?

Definition:

Two lines that intersect to form a right angle (90°) are called perpendicular lines.

Key Properties:

  • •Right angles: Perpendicular lines form four 90° angles at their intersection
  • •Unique perpendicular: Through any point on a line, there is exactly one perpendicular line
  • •Shortest distance: The perpendicular from a point to a line gives the shortest distance
  • •Symmetric property: If line a ⊥ line b, then line b ⊥ line a

Important Terms:

  • Perpendicular: The line that forms right angles with another line
  • Foot of perpendicular: The point where the perpendicular meets the original line
  • Perpendicular distance: The length of the perpendicular segment

Notation:

The symbol "⊥" represents perpendicular lines. For example: line a ⊥ line b (read as "line a is perpendicular to line b").

Real-World Examples:

  • • Walls meeting the floor
  • • The hands of a clock at 3:00 or 9:00
  • • Street intersections at corners
  • • The edges of a square or rectangle
Perpendicular Line Properties

Mathematical Properties:

Existence: Through any point, exactly one perpendicular to a given line exists
Uniqueness: The perpendicular from a point to a line is unique
Minimum distance: Perpendicular gives shortest path
Drawing Perpendicular Lines

Steps to Draw Perpendicular Lines:

  1. Draw the first line
  2. Place a protractor at the intersection point
  3. Mark 90° from the first line
  4. Draw the second line through this mark

Tips for Accurate Construction:

  • • Use a set square or protractor for precise 90° angles
  • • Ensure the intersection point is clearly marked
  • • Check that all four angles formed are equal (90° each)
  • • Practice with different starting line orientations
Applications of Perpendicular Lines

In Construction:

  • • Wall corners
  • • Door frames
  • • Foundation layouts
  • • Right-angle joints

In Design:

  • • Grid systems
  • • Coordinate planes
  • • Orthogonal layouts
  • • Technical drawings
Perpendicular vs Other Line Relationships
PropertyPerpendicular Lines (⊥)Parallel Lines (∥)
IntersectionIntersect at one pointNever intersect
Angle formed90° (right angles)No angles (don't meet)
DistanceShortest at intersectionConstant everywhere
DirectionDifferent directionsSame direction