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How do you make a parallelogram that is not a square from 4 identical isosceles right triangles?
Two isosceles right triangles, if joined hypotenuse-to-hypotenuse will make a square. Two squares, sided by side, make a rectangle which is a parallelogram, and not a square.
How do you make a rectangle with 2 triangles and two squares?
Draw a rectangle made with three squares. Then put a diagonal line through the center one. Tah-Dah
How do you make 2 squares and 4 triangles from 8 toothpicks?
make a circle
What are the regular polygons that make up a tesselation?
Triangles or squares or hexagons. There are also mixtures, like octagons plus squares.
Will a pattern of right triangles and squares tessellate?
Yes. Consider the situation when: the right-angled triangles are also isosceles and the hypotenuse (longest side) of the triangles is equal to the side of the square. If you surround a square with four of right-angled triangles (the sides of the square being in contact with the hypotenuses of the triangles), you get a larger shape which is also a square. Taking this as a basic unit, you can make a tesselations. You can also make tessalations if you have two sets of squares, one with sides the same length of the hypotenuse of the triangles and one with sides the same length as the smaller sides of the triangles.
