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Anti-parallel straight lines

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with respect to two given lines $m_1$ and $m_2$

Two straight lines $l_1$ and $l_2$ which intersect $m_1$ and $m_2$ so that $\angle1=\angle2$ (cf. Fig.).

Figure: a012660a

If $l_1$ and $l_2$ are anti-parallel with respect to $m_1$ and $m_2$, then $m_1$ and $m_2$ are also anti-parallel with respect to $l_1$ and $l_2$. In any quadrilateral inscribed in a circle, any two opposite sides are anti-parallel with respect to the other two sides. If the lines $m_1$ and $m_2$ intersect at a point $O$, one also says that $l_1$ and $l_2$ are anti-parallel with respect to the angle $m_1Om_2$. If the lines $m_1$ and $m_2$ coincide, $l_1$ and $l_2$ are said to be anti-parallel with respect to a straight line.

How to Cite This Entry:
Anti-parallel straight lines. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Anti-parallel_straight_lines&oldid=31542
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article