## Parallelo-hexagon with Obtuse Angles

Below is shown a dynamic sketch of a hexagon with opposite sides equal and parallel, i.e. a parallelo-hexagon. More-over, it has been constructed in such a way that all its angles are obtuse. Explore the sketch by dragging any of the red vertices or the points H and I to change the obtuse angles at vertices A and F.
Theorem: If ABCDEF is a convex parallelo-hexagon with all its angles obtuse, then the following inequality holds: AD² + BE² + CF² > 3(AB² + BC² + CD²).

#### .sketch_canvas { border: medium solid lightgray; display: inline-block; } Parallelo-hexagon with Obtuse Angles

Explaining
Can you EXPLAIN WHY (prove that) this theorem is true?

Explore More
To explore more about the relations between the sides and diagonals of parallelo-hexagons, or general hexagons, click on Relations between the sides and diagonals of parallelo-hexagons, and the general theorem of Douglas to navigate to a separate, accurately constructed dynamic sketch.

Reference
De Villiers, M. (2012). Relations between the sides and diagonals of a set of hexagons. Mathematical Gazette, July, 96(536), pp. 309-315.

Created, Michael de Villiers, 21 September 2023 using WebSketchpad.