This is a question from Kiselev's plane geometry book:
Four points on the plane are vertices of three quadrilaterals. Explain how this happens.
How do you explain this?
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asked Sep 2, 2018 at 17:14
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3 Answers
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You typically have the three options $$ ABCD, ABDC, ACBD$$
answered Sep 2, 2018 at 17:36
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1$\begingroup$ Difference in the order of letters only? $\endgroup$ Sep 2, 2018 at 17:37
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1$\begingroup$ @JamesWarthington Pick and label four "random" points, and connect hem to quadrilaterals in the three mentioned orders (always adding the back-t-start edge, of course) $\endgroup$ Sep 2, 2018 at 17:39
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If you want non-overlapping quadrilaterals, it will have to look something like this:
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Consider a tetrahedron in Euclidean space. Each edge is the common side of a pair of adjacent triangles and is also paired with its opposite edge which is the common side of another pair of adjacent triangles. The other four edges are common to both pairs of adjacent triangles and forms a quadrilateral in space. There are three such quadrilaterals associated with the three pairs of opposite edges. Project the tetrahedron onto a plane to get four points in the plane as projections of four vertices and its edges as three associated plane quadrilaterals.
