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?

Question

This is a question from Kiselev&#039;s plane geometry book:Four points on the plane are vertices of three quadrilaterals. Explain how this happens.How do you explain this?

Alaina Mcintosh · Accepted Answer

You typically have the three options  A  B  C  D  ,  A  B  D  C  ,  A  C  B  D

June Mejia · Accepted Answer

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.

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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