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2. Intercept theorem - Wikipedia

   en.wikipedia.org/wiki/Intercept_theorem

   The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.

3. Parallel (geometry) - Wikipedia

   en.wikipedia.org/wiki/Parallel_(geometry)

   Since these are equivalent properties, any one of them could be taken as the definition of parallel lines in Euclidean space, but the first and third properties involve measurement, and so, are "more complicated" than the second. Thus, the second property is the one usually chosen as the defining property of parallel lines in Euclidean geometry ...

4. Distance between two parallel lines - Wikipedia

   en.wikipedia.org/wiki/Distance_between_two...

   the distance between the two lines is the distance between the two intersection points of these lines with the perpendicular line y = − x / m . {\displaystyle y=-x/m\,.} This distance can be found by first solving the linear systems

5. Line (geometry) - Wikipedia

   en.wikipedia.org/wiki/Line_(geometry)

   For a convex quadrilateral with at most two parallel sides, the Newton line is the line that connects the midpoints of the two diagonals. [7] For a hexagon with vertices lying on a conic we have the Pascal line and, in the special case where the conic is a pair of lines, we have the Pappus line. Parallel lines are lines in the same plane that ...

6. Playfair's axiom - Wikipedia

   en.wikipedia.org/wiki/Playfair's_axiom

   Parallel Line: This second perpendicular line will be parallel to L by the definition of parallel lines (i.e the alternate interior angles are congruent as per the 4th axiom). The statement is often written with the phrase, "there is one and only one parallel". In Euclid's Elements, two lines are said to be parallel if they never meet and other ...

7. Westchester man, 55, stabbed to death at upscale NYC ... - AOL

   www.aol.com/news/westchester-man-stabbed-death...

   A 55-year-old Westchester County man was stabbed to death early Monday morning inside a ritzy Queens nightclub after he and the suspect got into an argument, police and law enforcement sources said.