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 The Complete Quadrilateral The mathematical object that goes by the name of complete quadrilateral is neither complete nor quadrilateral, at least not in the sense in which the word "quadrilateral" appears in, say, Brahmagupta's theorem about cyclic quadrilaterals. A complete quadrilateral is a configuration of four straight lines in general position and six points at which the lines intersect. First of all, we have the Theorem of Complete Quadrilateral: the midpoints of the three diagonals are collinear. www.cut-the-knot.org /ctk/CompleteQuadrilateral.shtml   (1612 words)

 PlanetMath: cyclic quadrilateral A quadrilateral is cyclic when its four vertices lie on a circle. A necessary and sufficient condition for a quadrilateral to be cyclic, is that the sum of a pair of opposite angles be equal to This is version 4 of cyclic quadrilateral, born on 2001-10-06, modified 2002-03-09. planetmath.org /encyclopedia/Cyclic.html   (170 words)

 Quadrilateral - LoveToKnow 1911 QUADRILATERAL, in geometry, a figure enclosed by four straight lines. But the most famous quadrilateral was that of the four fortified towns of north Italy - Mantua, Peschiera, Verona, and Legnago, FIG. The real value of the quadrilateral, which gave Austria such a firm hold on Lombardy, lay in the great natural strength of Mantua and in the readiness with which troops and supplies could be poured into Verona from the north. www.1911encyclopedia.org /Quadrilateral   (161 words)

 quadrilateral - Search Results - MSN Encarta Quadrilateral, in geometry, plane figure with four straight sides. The best-known quadrilaterals are the square, with four internal right angles,... Cyclic Quadrilateral, four-sided figure with all four of its vertices lying on the circumference of a circle. encarta.msn.com /quadrilateral.html   (164 words)

 cylic quadralerals The length of the two diagonals of a cyclic quadrilateral are related to the four sides in Ptolemy's Theorem which states (using m and n for the diagonals lengths) mn=ac+bd. The center of this "orthic cyclic quadrilateral" is the reflection of the circumcenter of the original quadrilateral in the anti-center. The anti-center of the orthic quadrilateral is the same as the anti-center of the original quadrilateral, and so the orthocenters of the triangles formed by the orthic quadrilateral are the vertices of the original cyclic quadrilateral. www.pballew.net /cycquad.html   (1589 words)

 Math Forum: Ask Dr. Math FAQ: Quadrilateral Formulas For other Americans, however, a trapezoid is a quadrilateral with one and only one pair of parallel sides, in which case a parallelogram is not a trapezoid. A quadrilateral all of whose vertices lie on a circle. Points A, B, C, and D lie on a circle of radius R. Sides a, b, c, and d are tangent to a circle of radius r. mathforum.org /dr.math/faq/formulas/faq.quad.html   (536 words)

 quadrilateral The quadrilateral, quadrangle or tetragon is a polygon with four sides. The tangent quadrilateral and the cyclic quadrilateral are special cases of the tangent polygon and the cyclic polygon. For the tangent quadrilateral the opposite sides are of equal length. www.2dcurves.com /line/lineq.html   (733 words)

 Quadrilateral - Search Results - MSN Encarta Quadrilateral, plane figure (that is, a shape drawn on a flat surface) bounded by four straight lines called its sides. Cyclic Quadrilateral, four-sided figure (quadrilateral) with all four of its vertices lying on the circumference of a circle. Trapezium, in plane geometry, quadrilateral (four-sided) figure with two parallel sides, or bases, generally of unequal length. uk.encarta.msn.com /Quadrilateral.html   (106 words)

 Cyclic Quadrilateral -- from Wolfram MathWorld A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex. A quadrilateral that can be both inscribed and circumscribed on some pair of circles is known as a bicentric quadrilateral. The diagonals of a cyclic quadrilateral have lengths mathworld.wolfram.com /CyclicQuadrilateral.html   (511 words)

 Wesleyan Quadrilateral - Wikipedia, the free encyclopedia The Wesleyan Quadrilateral is a methodology for theological reflection that is credited to John Wesley, leader of the Methodist movement in the late 18th Century. Each of the "legs" of the Wesleyan Quadrilateral must be taken in balance, and none of the other three apart from scripture should be viewed as being of equal value or authority with scripture. The Wesleyan Quadrilateral in John Wesley by Albert C. Outler en.wikipedia.org /wiki/Wesleyan_Quadrilateral   (708 words)

 Quadrilateral -- from Wolfram MathWorld A quadrilateral with two sides parallel is called a trapezoid, whereas a quadrilateral with opposite pairs of sides parallel is called a A special type of quadrilateral is the cyclic quadrilateral, for which a circle can be circumscribed so that it touches each polygon vertex. Another special type is a tangential quadrilateral, for which a circle and be inscribed so it is tangent to each edge. mathworld.wolfram.com /Quadrilateral.html   (651 words)

 Quadrilateral - Wikipedia, the free encyclopedia Square (regular quadrilateral): four sides have equal length, and each angle is a right angle. Cyclic quadrilateral: the four vertices lie on a circumscifed circle. Tangential quadrilateral: the four edges are tangential to an inscribed circle. en.wikipedia.org /wiki/Quadrilateral   (557 words)

 Spring 2003 Issue In order for the Wesleyan quadrilateral to serve as a resource for contemporary discipleship, we must first be clear about its role in the life of The United Methodist Church. Unfortunately, at times, the quadrilateral is mistakenly thought to replace or supersede our doctrinal standards or the basics that John Wesley, and subsequent generations of Wesleyans, held to be so essential for growing as disciples of Jesus Christ. The quadrilateral provides a bridge between the beliefs of our heritage and the context of our contemporary situation, such that we do not have to choose between living either as "traditional" Christians or as "postmodern" ones. www.gbod.org /smallgroup/covenant/spring03/foursome.html   (1432 words)

 Illuminations: Diagonals to Quadrilaterals Launch the Diagonals to Quadrilaterals I applet, either as a whole-class activity or as pairs of students working on a computer. Ask students what types of quadrilaterals are possible, and have them list the possibilities on their whiteboards. Students may see that the initial shape is a general quadrilateral; others may drag the points to create a kite, a rhombus, or even what appears to be a square. illuminations.nctm.org /LessonDetail.aspx?ID=L655   (1429 words)

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