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Paving Paths

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LOGO Challenge 5 - Patch

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

Tessellating Hexagons

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Is it true that any convex hexagon will tessellate if
  • it has a pair of opposite sides that are equal, and
  • three adjacent angles that add up to 360 degrees?

You may assume that the adjacent angles that add up to 360 degrees are "in between" the equal sides, as shown in the diagram.

image of hexagon
Can you show that it will always be true?

Can you find a counter example?

This problem appears in "Tiles and Tiling", an activity book published by the Association of Teachers of Mathematics