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Squares.

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Q: The addition of what shape will allow regular octagons to tessellate?
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Can heptagon tessellate?

No. Equilateral heptagons (7 sided figures) do not tessellate the plane. Not if no other polygons are allowed. But if you allow a (non-equilateral) pentagon then you might be able to tessellate the plane!


Can a semicircle tessellate with other shapes?

Yes. Any shape can tessellate if you allow other shapes. The simplest way is to select the other shapes so that the given shape and the "other shapes" can be combined to make a rectangle or square.


Why can't some shapes tessellate?

A "tessellation" (also called a "tiling") of a plane region is a covering of that 2-dimensional region using shapes that don't overlap and don't leave any gaps uncovered. Typically, we are interested in trying to use shapes that are congruent (all the same size and shape) regular polygons (the angles and sides of each polygon are the same), such as an equilateral triangle, a square, a regular pentagon, etc. This is called a "regular tessellation". It has been shown that the only regular polygons that tessellate are equilateral triangles, squares, and hexagons. So for example, a regular pentagon can't be used to tile a floor, because the angles don't match up as needed and will leave gaps on the floor that would need a different shape to fill them in. Consider, for example, a regular octagon. Each interior angle is 135o. So if you put two octagons next to each other, sharing a common side, then the two interior angles would combine to be 270o. But that leaves only another 90o of the full 360o at the point the two edges meet and need another shape to complete the tiling, which is not enough room to squeeze in another octagon that would take up 135o. The 90o does allow enough room for a square, however, and in fact octagons and squares can be combined to tile a floor in what is called a "semiregular tessellation" (using more than one shape).


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Does the Constitution allow the addition of new states?

Yes


The Constitution does not allow the addition of new states?

it is false!!


What part of speech is to allow?

The word allow is a regular verb. The past tense is allowed.


Do parallelograms tesselate?

Yes. Remember that rectangles and squares are both parallelograms. Square tiles are the most common. The next most common are rectangles. Both shapes can tessellate finite planes. Other parallelograms can tessellate infinite planes (or finite ones if you allow parts of the parallelogram along the edge of the plane.)


Where can I print off addition worksheets online?

There are several good websites that provide printable addition worksheets. Try APlusMath.com. They allow you to print customized addition worksheets.


Does Jenny Craig allow regular meals and snacks?

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Does the eating plan allow regular meals and snack?

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How can addition properties help you add whole numbers?

Because addition properties allow you to add them in the first place and without them, you couldn't add!