Question

How can you make a quadrilateral rigid?

Answer 1

Add a cross brace connecting two parts of the quadrilateral, avoiding some non-rigid cases.

Explanation:

Any quadrilateral is naturally non-rigid.

The simplest cross brace to describe that will render a convex quadrilateral non rigid is to add a line segment from one vertex to the opposite one. This will subdivide the quadrilateral into two rigid triangles.

It is possible to make a quadrilateral rigid with a cross brace that connects a point on one side to another point on the quadrilateral, but this does not always result in a rigid structure.

For example, a line segment joining the mid point of one side of a rectangle to the midpoint of the opposite side would not make the structure more rigid.

On the other hand, if you have a line segment that runs from `1/3` of the way along one side to `2/3` of the way along the opposite side, then the resulting structure would be rigid.