page_title: Newton–Gauss line
section_title: Two cyclic quadrilaterals sharing a Newton-Gauss line
hierarchical_section_title: Newton–Gauss line / Applications to cyclic quadrilaterals / Two cyclic quadrilaterals sharing a Newton-Gauss line
caption_attribution_description: English: Showing that MPHN and MQHN are cyclic
context_page_description: In geometry, the Newton–Gauss line is the line joining the midpoints of the three diagonals of a complete quadrilateral.
  The midpoints of the two diagonals of a convex quadrilateral with at most two parallel sides are distinct and thus determine a line, the Newton line. If the sides of such a quadrilateral are extended to form a complete quadrangle, the diagonals of the quadrilateral remain diagonals of the complete quadrangle and the Newton line of the quadrilateral is the Newton–Gauss line of the complete quadrangle.
caption: Figure 3: Showing that the quadrilaterals MPGN and MQHN are cyclic.
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