You should look into right triangles. They are particularly useful when creating a tessellation.
Example rug:
Property: Rigid motions
Practice makes perfect
The easiest triangle we can use is a right triangle. This is simply half a rectangle which will make it easier to create our rug.
A possible rug could be the one below.
The property that guarantees the congruence of the triangle is called "rigid motions". By only using translations, reflections, or rotations when copying the triangle, we preserve the triangles angle and side measure. For this particular figure, we have reflected the triangle using either the triangles hypotenuse or its legs as line of reflection.
