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LOGO Challenge 5 - Patch

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

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Sharks Are Symmetric

Weekly Problem 35 - 2012
How many more triangles need to be shaded to make the pattern have a line of symmetry?

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Hexagon Cut Out

Weekly Problem 52 - 2012
An irregular hexagon can be made by cutting the corners off an equilateral triangle. How can an identical hexagon be made by cutting the corners off a different equilateral triangle?

Can You Explain Why?

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Imagine having a pencil, ruler, protractor and compass and being asked to draw the triangle below.

Can you explain why it is an impossible triangle to construct?