Which of the following is true if a pentagon tessellates a plane?
a. A pentagon never tessellates a plane
b. All of its sides must be the same length
c. It must be a regular pentagon
d. It has one pair of parallel slides
Note that the tessellation required did not mention a regular pentagon.
Examine the two examples shown in the following link, and make conclusions accordingly.
http://img504.imageshack.us/img504/9859/tessellationwithapentag.png
To determine which of the options is true if a pentagon tessellates a plane, let's understand the concept of tessellation and the properties of a pentagon.
Tessellation, also known as tiling, is the process of covering a plane with repeated shapes without any gaps or overlaps. In this case, we are considering if a pentagon can be used to fully cover a plane.
Here are the properties of the options provided:
a. A pentagon never tessellates a plane: This statement is not necessarily true. Some polygons can tessellate a plane, while others cannot. We need to explore further before confirming if a pentagon tessellates a plane or not.
b. All of its sides must be the same length: While this statement is true for a regular pentagon, it is not a requirement for tessellation. Tessellation is possible with irregular polygons as well.
c. It must be a regular pentagon: This statement is not necessarily true. Regular polygons have all sides and angles equal, which makes them an obvious choice for tessellation. However, there are irregular pentagons that can also tessellate a plane.
d. It has one pair of parallel slides: This statement refers to the presence of parallel sides, which is a property of parallelograms, not pentagons. Therefore, this statement is not true.
Considering the options provided, the only statement that is not necessarily true is option (a) – "A pentagon never tessellates a plane." There are specific irregular pentagons that can tessellate a plane.
In conclusion, the correct answer is none of the provided options since a pentagon can tessellate a plane, but none of the statements in the options are entirely accurate.