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The-diagonals-of-a-convex-quadrilateral-divide-the-area-into-A-B-D-and-C-numbered-clockwise-such-that-A-B-C-D-Does-this-theorem-have-a-name-




Question Number 137314 by liberty last updated on 01/Apr/21
  The diagonals of a convex quadrilateral divide the area into A, B, D and C (numbered clockwise) such that A/B = C/D. Does this theorem have a name?
$$ \\ $$The diagonals of a convex quadrilateral divide the area into A, B, D and C (numbered clockwise) such that A/B = C/D. Does this theorem have a name?
Commented by mr W last updated on 01/Apr/21
it′s so obviours that i think there is  no special name for it. there is also  no special name for the theorem that  the sum of all internal angles of a  quadrilateral is 360°.
$${it}'{s}\:{so}\:{obviours}\:{that}\:{i}\:{think}\:{there}\:{is} \\ $$$${no}\:{special}\:{name}\:{for}\:{it}.\:{there}\:{is}\:{also} \\ $$$${no}\:{special}\:{name}\:{for}\:{the}\:{theorem}\:{that} \\ $$$${the}\:{sum}\:{of}\:{all}\:{internal}\:{angles}\:{of}\:{a} \\ $$$${quadrilateral}\:{is}\:\mathrm{360}°. \\ $$
Answered by EDWIN88 last updated on 01/Apr/21
Sure it has a name , Dunkley′s Theorem.  ′ The diagonals of convex quadrilateral ABCD  divide the quadrilateral into four triangles  ; the products of areas of the opposing   triangles are equal.′
$$\mathrm{Sure}\:\mathrm{it}\:\mathrm{has}\:\mathrm{a}\:\mathrm{name}\:,\:\mathrm{Dunkley}'\mathrm{s}\:\mathrm{Theorem}. \\ $$$$'\:\mathrm{The}\:\mathrm{diagonals}\:\mathrm{of}\:\mathrm{convex}\:\mathrm{quadrilateral}\:\mathrm{ABCD} \\ $$$$\mathrm{divide}\:\mathrm{the}\:\mathrm{quadrilateral}\:\mathrm{into}\:\mathrm{four}\:\mathrm{triangles} \\ $$$$;\:\mathrm{the}\:\mathrm{products}\:\mathrm{of}\:\mathrm{areas}\:\mathrm{of}\:\mathrm{the}\:\mathrm{opposing}\: \\ $$$$\mathrm{triangles}\:\mathrm{are}\:\mathrm{equal}.'\: \\ $$

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