Perpendicular

In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). The property extends to other related geometric objects.

A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if (1) the two lines meet; and (2) at the point of intersection the straight angle on one side of the first line is cut by the second line into two congruent angles. Perpendicularity can be shown to be symmetric, meaning if a first line is perpendicular to a second line, then the second line is also perpendicular to the first. For this reason, we may speak of two lines as being perpendicular (to each other) without specifying an order.

Perpendicularity easily extends to segments and rays. For example, a line segment \overline{AB} is perpendicular to a line segment \overline{CD} if, when each is extended in both directions to form an infinite line, these two resulting lines are perpendicular in the sense above. In symbols, \overline{AB} \perp \overline{CD} means line segment AB is perpendicular to line segment CD. The point B is called a foot of the perpendicular from A to segment \overline{CD}, or simply, a foot of A on \overline{CD}.

Perpendicular (disambiguation)

Perpendicular may refer to:

  • Perpendicular, in mathematics two lines at right angles
  • Perpendicular axis theorem
  • Perpendicular Period, style and period of mediaeval English Gothic architecture
  • Perpendicular plate of ethmoid bone
  • Perpendicular plate of palatine bone
  • Perpendicular Point, New Zealand
  • Perpendicular recording, disc drive technology
  • See also

  • Point Perpendicular, New South Wales, Australia
  • Purpendicular, music album by Deep Purple
  • English Gothic architecture

    English Gothic is the name of the architectural style that flourished in England from about 1180 until about 1520.

    As with the Gothic architecture of other parts of Europe, English Gothic is defined by its pointed arches, vaulted roofs, buttresses, large windows, and spires. The Gothic style was introduced from France, where the various elements had first been used together within a single building at the choir of the Basilique Saint-Denis north of Paris, built by the Abbot Suger and dedicated on 11 June 1144. The earliest large-scale applications of Gothic architecture in England are at Canterbury Cathedral and Westminster Abbey. Many features of Gothic architecture had evolved naturally from Romanesque architecture (often known in England as Norman architecture). This evolution can be seen most particularly at the Norman Durham Cathedral, which has the earliest pointed ribbed high vault known.

    English Gothic was to develop along lines that sometimes paralleled and sometimes diverged from those of continental Europe. Historians traditionally divide English Gothic into a number of different periods, which may be further subdivided to accurately define different styles. Gothic architecture continued to flourish in England for a hundred years after the precepts of Renaissance architecture were formalised in Florence in the early 15th century. The Gothic style gave way to the Renaissance in the later 16th and 17th centuries, but was revived in the late 18th century as an academic style and had great popularity as Gothic Revival architecture throughout the 19th century.

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    Lesson 50 Perpendicular and Parallel Lines Geometry

    Bitchute 23 Mar 2025
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