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For a parallelogram, the Newton line does not exist since both midpoints of the diagonals coincide with point of intersection of the diagonals. Moreover, the area identity of the theorem holds in this case for any inner point of the quadrilateral.
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The converse of Anne's theorem is true as well, that is for any point on the Newton line which is an inner point of the quadrilateral, the area identity holds.
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224:{\displaystyle \left|\triangle BCL\right|+\left|\triangle DAL\right|=\left|\triangle LAB\right|+\left|\triangle DLC\right|,}
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if the two sums of the areas of opposing triangles are equal, according to Anne's theorem.
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114:. If the two sums of areas of opposite triangles are equal:
31:. This theorem is named after the French mathematician
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27:describes an equality of certain areas within a
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59:The theorem is stated as follows: Let
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350:The Converse of Leon Anne's Theorem
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341:Newton's and Léon Anne's Theorems
63:be a convex quadrilateral with
277:A Cornucopia of Quadrilaterals
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392:Theorems about quadrilaterals
16:Theorem in Euclidean geometry
282:American Mathematics Society
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313:Cambridge University Press
94:of the diagonals, and let
308:More Mathematical Morsels
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368:"Leon Anne's Theorem"
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315:. pp. 174–175.
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29:convex quadrilateral
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82:. Furthermore, let
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258:References
373:MathWorld
202:△
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108:triangles
92:midpoints
65:diagonals
39:Statement
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354:Archived
47:A point
90:be the
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317:ISBN
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243:and
112:ABCD
100:ABCD
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19:In
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