Wikipedia says that
The shape of a simple quadrilateral is fully determined by the lengths of its sides and one diagonal.
but I have my doubts. For example, the two quadrilaterals in this picture both have the same side lengths and the same yellow diagonal, but are not the same.
Am I missing something here, or are simple quadrilaterals not actually determined (all sides and angles) by the lengths of four sides and a diagonal? If not, what about a convex quadrilateral? Would that be fully determined by those lengths?
Best Answer
The wikipedia article specifies that the polygon is convex in almost every paragraph of this article.
It is only true for a convex polygon, you just proved that wikipedia can be wrong :).
For a convex polygon i can think of the following proof :
With 4 lengths and 1 diagonal you define 2 unique triangles (a triangle is uniquely defined by the length of his 3 sides) with one common side, and therefore one unique polygon.