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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?

Commented by mr W last updated on 01/Apr/21

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

Answered by EDWIN88 last updated on 01/Apr/21

$$\mathrm{Sure}\mathrm{it}\mathrm{has}\mathrm{a}\mathrm{name},{\mathrm{Dunkley}}^{\prime }\mathrm{s}\mathrm{Theorem}.$$$${}^{\prime }\mathrm{The}\mathrm{diagonals}\mathrm{of}\mathrm{convex}\mathrm{quadrilateral}\mathrm{ABCD}$$$$\mathrm{divide}\mathrm{the}\mathrm{quadrilateral}\mathrm{into}\mathrm{four}\mathrm{triangles}$$$$;\mathrm{the}\mathrm{products}\mathrm{of}\mathrm{areas}\mathrm{of}\mathrm{the}\mathrm{opposing}$$$$\mathrm{triangles}\mathrm{are}\mathrm{equal}{.}^{\prime }$$

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