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| {{too technical|date=November 2012}}
| | Her title is Felicidad Ahmad. Bookkeeping has been his day job for a whilst. Some time ago he selected to reside in Kansas. Playing crochet is some thing that I've carried out for many years.<br><br>Here is my page [http://bjjoutlet.com/UserProfile/tabid/43/userId/20679/Default.aspx auto warranty] |
| In [[geometry]], '''anti-parallel lines''' can be defined with respect to either lines or angles.
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| ==Definitions==
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| [[File:anti1.svg|thumb|right|Given two lines <math>m_1 \,</math> and <math>m_2 \,</math>, lines <math>l_1 \,</math> and <math>l_2 \,</math> are anti-parallel with respect to <math>m_1 \,</math> and <math>m_2 \,</math> if <math>\angle 1 = \angle 2 \,</math>. ]]
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| Given two lines <math>m_1 \,</math> and <math>m_2 \,</math>, lines <math>l_1 \,</math> and <math>l_2 \,</math> are anti-parallel with respect to <math>m_1 \,</math> and <math>m_2 \,</math> if <math>\angle 1 = \angle 2 \,</math>. If <math>l_1 \,</math> and <math>l_2 \,</math> are anti-parallel with respect to <math>m_1 \,</math> and <math>m_2 \,</math>, then <math>m_1 \,</math> and <math>m_2 \,</math> are also anti-parallel with respect to <math>l_1 \,</math> and <math>l_2 \,</math>.
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| In any [[quadrilateral]] inscribed in a circle, any two opposite sides are anti-parallel with respect to the other two sides.
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| [[File:anti5.svg|thumb|right|In any quadrilateral inscribed in a circle, any two opposite sides are anti-parallel with respect to the other two sides. ]]
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| Two lines <math>l_1 \,</math> and <math>l_2 \, </math>are said to be antiparallel with respect to the sides of an angle if they make the same angle <math>\angle APC</math> in the opposite senses with the [[bisector]] of that angle.
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| [[File:anti2.svg|thumb|right|Two lines <math>l_1 \,</math> and <math>l_2 \, </math> are said to be antiparallel with respect to the sides of an angle if they make the same angle <math>\angle APC</math> in the opposite senses with the bisector of that angle. Notice that our previous angles 1 and 2 are still equivalent. ]]
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| [[File:anti3.svg|thumb|right|If the lines <math>m_1 \,</math> and <math>m_2 \,</math> coincide, <math>l_1 \,</math> and <math>l_2 \, </math> are said to be anti-parallel with respect to a straight line.]]
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| ===Antiparallel vectors===
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| In a [[vector space]] over <math> \mathbb{R} </math> (or some other [[ordered field]]),
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| two nonzero vectors are called antiparallel if they are parallel but have opposite directions.<ref>{{cite book
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| |title=Handbook of mathematics and computational science
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| |first1=John
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| |last1=Harris
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| |first2=John W.
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| |last2=Harris
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| |first3=Horst
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| |last3=Stöcker
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| |publisher=Birkhäuser
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| |year=1998
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| |isbn=0-387-94746-9
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| |page=332
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| |url=http://books.google.com/books?id=DnKLkOb_YfIC}}, [http://books.google.com/books?id=DnKLkOb_YfIC&pg=PA332 Chapter 6, p. 332]
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| </ref>
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| In that case, one is a [[negative number|negative]] [[scalar (mathematics)|scalar]] times the other.
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| ==Relations==
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| # The line joining the feet to two altitudes of a triangle is antiparallel to the third side.(any cevians which 'see' the third side with the same angle create antiparallel lines)
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| # The tangent to a triangle's [[circumcircle]] at a vertex is antiparallel to the opposite side.
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| # The radius of the circumcircle at a vertex is perpendicular to all lines antiparallel to the opposite sides.
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| ==References==
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| {{reflist}}
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| *A.B. Ivanov, Encyclopaedia of Mathematics - ISBN 1-4020-0609-8
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| *Weisstein, Eric W. "Antiparallel." From MathWorld--A Wolfram Web Resource. [http://mathworld.wolfram.com/Antiparallel.html]
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| [[Category:Elementary geometry]]
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