# Two Geometry Puzzles

October 11, 2020 pm31 11:59 pm

I haven’t asked a math question in a long, long time. Not sure if anyone who does them is still reading…

**Can a Polygon Be Constructed?**

Under what circumstances is it possible, given n ≥ 3 segments, to form a polygon?

Or, if you prefer, under what circumstances, given n ≥ 3 segments, is it not possible to form a polygon?

The segments may be connected in any order.

**Can a Quadrilateral, but not a Trapezoid, be Formed?**

Are there four segments from which it is possible to construct a quadrilateral, but from which it is not possible to construct a trapezoid?

The segments may be connected in any order.

Trapezoid is new to me, I’ll have to think about it when I’m more awake!

I thought about clarifying which definition of trapezoid, but not necessary.

https://jd2718.org/2014/05/26/politicizing-the-trapezoid/

Ha! It does change the answer, though, doesn’t it?

Okay, so, I am fairly confident that I know the answer for (b). I am pretty confident that I could work out the associated (messy?) algebra, but I wonder if there’s a good conceptual proof. Something with hinges?

I finally (!!) wrote something up: https://jblblog.wordpress.com/2021/08/23/trapezoids-and-blogs/