Definition

1. Noun:
   • The quality or state of being perpendicular: The condition of being at a right angle (90 degrees) to a given line or plane.
   • The relation of opposition between things at right angles: A formal or geometric relationship describing two lines or planes that intersect at a 90-degree angle.

Usage Examples

• Noun:
  • The architect checked the perpendicularity of the wall to the floor.
  • The carpenter ensured the perpendicularity of the two pieces of wood before joining them.
  • In geometry, we prove the perpendicularity of two lines using theorems.

Advanced Usage

• Mathematical/Geometric Context: Used to describe an essential property in Euclidean geometry, construction, and engineering.
  • The theorem establishes the conditions for the perpendicularity of a line to a plane.
• Figurative/Formal Context: Can describe a relationship of direct opposition or stark contrast, extending from the geometric meaning.
  • There was a certain perpendicularity between their political ideologies. (This usage is less common and more literary.)

Variants and Related Words

• Perpendicular (adj/noun): At an angle of 90° to a given line, plane, or surface; also, a perpendicular line or position.
  • The ladder should be perpendicular to the ground.
• Perpendicularly (adverb): In a perpendicular direction or manner.
  • The tower rose perpendicularly from the base.

Synonyms

• Orthogonality: (Technical, especially in mathematics) The condition of being perpendicular.
• Right-angledness: The state of forming a right angle (less common synonym).

Antonyms

• Parallelism: The state of being parallel, meaning lines or planes that are always the same distance apart and do not meet.
• Obliqueness: The state of being at an angle that is not a right angle; slanting.

Related Phrases/Concepts

• At right angles: A phrase describing perpendicularity.
  • The two streets intersect at right angles.
• Normal to a plane: (Technical) A line that is perpendicular to a plane.
  • The force vector is normal to the surface.

Noun

1. the quality of being at right angles to a given line or plane (especially the plane of the horizon)
2. the relation of opposition between things at right angles