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• Geometric inequality
  ...involving various measures ([[angle]]s, [[length]]s, [[area]]s, etc.) in [[geometry]]. ...ality is particularly useful and shows up frequently on Intermediate level geometry problems. It also provides the basis for the definition of a [[metric spac
  7 KB (1,300 words) - 01:11, 28 October 2024
• Brahmagupta's Formula
  ...a's Formula''' is a [[formula]] for determining the [[area]] of a [[cyclic quadrilateral]] given only the four side [[length]]s, given as follows: <cmath>[ABCD] = \ [[Bretschneider's formula]] gives a formula for the area of a non-cyclic quadrilateral given only the side lengths; applying [[Ptolemy's Theorem]] to Bretschneide
  3 KB (543 words) - 19:35, 29 October 2024
• Ptolemy's theorem
  ...es a relationship between the side lengths and the diagonals of a [[cyclic quadrilateral]]; it is the [[equality condition | equality case]] of [[Ptolemy's Inequali Given a [[cyclic quadrilateral]] <math>ABCD</math> with side lengths <math>{a},{b},{c},{d}</math> and [[di
  6 KB (922 words) - 17:34, 13 January 2025
• Cyclic quadrilateral
  A '''cyclic quadrilateral''' is a [[quadrilateral]] that can be inscribed in a [[circle]]. While all [[triangles]] are cyclic In a quadrilateral <math>ABCD</math>:
  1 KB (179 words) - 19:41, 3 January 2025
• 1970 IMO Problems/Problem 6
  the convex hull of the <math>4</math>-gon is a quadrilateral, then at least [[Category:Olympiad Geometry Problems]]
  6 KB (1,054 words) - 18:09, 11 December 2024
• Quadrilateral
  A '''quadrilateral''' is a four-sided [[polygon]]. A kite is a quadrilateral with two pairs of adjacent [[congruent]] [[edge]]s.
  1 KB (167 words) - 20:14, 16 January 2025
• Orthic triangle
  In [[geometry]], given any <math>\triangle ABC</math>, let <math>D</math>, <math>E</math> ...yclic]]. These cyclic quadrilaterals make frequent appearances in olympiad geometry and are the most crucial section of this article.
  8 KB (1,408 words) - 09:39, 10 July 2024
• Square (geometry)
  A '''square''' is a [[quadrilateral]] in which all [[edge|sides]] have equal length and all [[angle | angles]] * [[Cube (geometry) | Cube]]
  1 KB (170 words) - 18:31, 3 September 2024
• Ptolemy's Inequality
  with equality if and only if <math>ABCD</math> is a cyclic quadrilateral with diagonals <math>AC </math> and <math>BD </math> OR if <math>A, B, C, D ...h>BDC </math> are [[congruent]], i.e., that <math>ABCD </math> is a cyclic quadrilateral.
  3 KB (602 words) - 09:01, 7 June 2023
• Polygon
  | [[quadrilateral|4]] * [[Geometry]]
  2 KB (372 words) - 19:04, 30 May 2015
• Bretschneider's formula
  Suppose we have a [[quadrilateral]] with [[edge]]s of length <math>a,b,c,d</math> (in that order) and [[diago It can be derived with [[vector]] [[geometry]].
  3 KB (566 words) - 03:51, 12 February 2021
• Law of Sines
  Let <math>ABCD </math> be a convex quadrilateral with <math>AB=BC=CD </math>, <math>AC \neq BD </math>, and let <math>E </ma * [[Geometry]]
  4 KB (658 words) - 21:52, 4 February 2025
• Area
  == Area of a Quadrilateral == To find the area of most [[quadrilateral]]s, you must divide the quadrilateral up into smaller triangles and find the area of each triangle. However, som
  7 KB (1,185 words) - 20:48, 25 November 2024
• Rectangle
  A '''rectangle''' is a [[quadrilateral]] in which all [[angle]]s are [[right angle]]s. ...e properties of a parallelogram. In addition, rectangles have [[congruent (geometry)|congruent]] [[diagonal]]s.
  782 bytes (108 words) - 13:36, 6 March 2022
• Parallelogram
  A '''parallelogram''' is a [[quadrilateral]] in which both pairs of opposite sides are parallel. Its properties inclu * Opposite sides are [[congruent (geometry) | congruent]].
  910 bytes (122 words) - 21:48, 13 November 2024
• Rhombus
  ...It is defined as a [[quadrilateral]] all of whose sides are [[congruent (geometry) | congruent]]. It is a special type of [[parallelogram]], and its propert ...rhombus' [[angle]]s are [[right angle]]s, then the rhombus is a [[square (geometry) | square]].
  3 KB (490 words) - 15:30, 22 February 2024
• Kite
  ...Thus, there are two types of quadrilaterals with two pairs of [[congruent (geometry) | congruent]] [[edge]]s, the [[parallelogram]] (if the members of each pai [[Category:Geometry]]
  784 bytes (122 words) - 13:09, 22 July 2024
• Trapezoid
  ...l and pretty geometric figure that lies in a plane. It is also a type of [[quadrilateral]]. *[[Quadrilateral]]
  1 KB (246 words) - 10:54, 2 January 2024
• 2006 AIME I Problems/Problem 1
  In [[quadrilateral]] <math>ABCD</math>, <math>\angle B</math> is a [[right angle]], [[diagonal [[Category:Introductory Geometry Problems]]
  1 KB (174 words) - 16:10, 3 February 2025
• 2006 AMC 10A Problems/Problem 17
  ...addition, <math>AH=AC=2</math>, and <math>AD=3</math>. What is the area of quadrilateral <math>WXYZ</math> shown in the figure? By symmetry, quadrilateral <math>WXYZ</math> is a square, so its area is
  6 KB (1,106 words) - 10:20, 4 November 2024

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