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?
Commented by mr W last updated on 01/Apr/21
$${it}'{s}\:{so}\:{obviours}\:{that}\:{i}\:{think}\:{there}\:{is} \\ $$$${no}\:{special}\:{name}\:{for}\:{it}.\:{there}\:{is}\:{also} \\ $$$${no}\:{special}\:{name}\:{for}\:{the}\:{theorem}\:{that} \\ $$$${the}\:{sum}\:{of}\:{all}\:{internal}\:{angles}\:{of}\:{a} \\ $$$${quadrilateral}\:{is}\:\mathrm{360}°. \\ $$
Answered by EDWIN88 last updated on 01/Apr/21
$$\mathrm{Sure}\:\mathrm{it}\:\mathrm{has}\:\mathrm{a}\:\mathrm{name}\:,\:\mathrm{Dunkley}'\mathrm{s}\:\mathrm{Theorem}. \\ $$$$'\:\mathrm{The}\:\mathrm{diagonals}\:\mathrm{of}\:\mathrm{convex}\:\mathrm{quadrilateral}\:\mathrm{ABCD} \\ $$$$\mathrm{divide}\:\mathrm{the}\:\mathrm{quadrilateral}\:\mathrm{into}\:\mathrm{four}\:\mathrm{triangles} \\ $$$$;\:\mathrm{the}\:\mathrm{products}\:\mathrm{of}\:\mathrm{areas}\:\mathrm{of}\:\mathrm{the}\:\mathrm{opposing}\: \\ $$$$\mathrm{triangles}\:\mathrm{are}\:\mathrm{equal}.'\: \\ $$