# How can $4$ points in the plane be vertices of $3$ different quadrilaterals?

Four points on the plane are vertices of three different quadrilaterals. How can this happen?

The problem is taken from "Kiselev's Geometry - Book I : Planimetry"

At first, I thought it could be like this :

But, the way diagonals are defined in the book:

Makes me think that the 3 figures I drew, are the same quadrilateral.

How do you think four points on the plane can be vertices of three different quadrilaterals

• Let A, B, C, D be the vertices. Then ABCD, ACDB, ADBC are three different quadrilaterals. The roles of sides and diagonals are not the same in them: there are 6 segments, and you can choose any two of them as diagonals, as long as they share no vertex (three possibilities to do so). – Jean-Claude Arbaut Dec 30 '17 at 20:11