# What kind of quadrilateral is determined by four sides and a diagonal?

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?

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Perhaps what is meant is not either of the diagonals, but (at least) one of them. – Benjamin Dickman Nov 6 '12 at 8:34
If by "lengths" of the sides one means the lengths in say counterclockwise order, then the lengths of the sides together with the length of a diagonal to specified vertices does determine the quadrilateral if it is convex. Your example shows the result is not true if we drop convexity. The Wikipedia article specifies simple here, and "simple" does not imply convex. So, a mistake. – André Nicolas Nov 6 '12 at 8:38