4.7 Dynamic Illustration of the Definition of a Simple Hexagon
The human brain is the best pattern recognizer in history
—Heinz-Karl Winkler

Definition. A simple hexagon ABCDEF is a set of six distinct points A, B, C, D, E, F, no three collinear, called vertices, and the six distinct lines AB, BC, CD, DE, EF, FA, called sides. The pairs of points A and D, B and E, and C and F are called opposite vertices. The three pairs of lines determined by opposite vertices are called diagonal lines. The pairs of lines AB and DE, BC and EF, and CD and FA are called opposite sides. The three points of intersection of the opposite sides are called diagonal points.

        In the figures of simple hexagon ABCDEF, the points I, J, and K are diagonal points and the light blue lines are diagonal lines.

Drag the red points to see the simple hexagon ABCDEF in many different positions.
To reset to the original settings, type the letter "R" on the keyboard.

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The Geometer's Sketchpad.