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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?\n

Commented bymr W last updated on 01/Apr/21

$${it}^{\prime }ssoobvioursthatithinkthereis$$ $$nospecialnameforit.thereisalso$$ $$nospecialnameforthetheoremthat$$ $$thesumofallinternalanglesofa$$ $$quadrilateralis360°.$$

Answered by EDWIN88 last updated on 01/Apr/21

$$\mathrm{Sure}\mathrm{it}\mathrm{has}\mathrm{a}\mathrm{name},\mathrm{D}\mathrm{u}\mathrm{n}\mathrm{k}\mathrm{l}\mathrm{e}\mathrm{y}{}^{\prime }\mathrm{s}\mathrm{T}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{m}.$$ $${}^{\prime }\mathrm{The}\mathrm{diagonals}\mathrm{of}\mathrm{convex}\mathrm{quadrilateral}\mathrm{ABCD}$$ $$\mathrm{divide}\mathrm{the}\mathrm{quadrilateral}\mathrm{into}\mathrm{four}\mathrm{triangles}$$ $$;\mathrm{the}\mathrm{products}\mathrm{of}\mathrm{areas}\mathrm{of}\mathrm{the}\mathrm{opposing}$$ $$\mathrm{triangles}\mathrm{are}\mathrm{equal}{.}^{\prime }$$

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