SOLUTION: 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 pen
Algebra.Com
Question 446057: 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
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
It is possible for a pentagon to tessellate a plane. Draw a "house" shaped pentagon:
Place several of these side by side, same orientation, then reflect the pentagon to tessellate the plane. Given this, we know that statements a and c need not be true.
The ability to tessellate the plane was not dependent on the sides being the same length either, so choice b is not true either. This leaves the only remaining choice, d.
A greater challenge: Can you prove that statement d must be true, without using process of elimination?
RELATED QUESTIONS
what is the perimeter of a pentagon
(answered by Euler)
Which of the following statement is ture?
A.Each interior angle of a regular pentagon... (answered by cuteminiming,solver91311,vleith)
Explain why a regular pentagon cannot tessellate a... (answered by fractalier,cleomenius)
Which of the two-dimensional cross sections listed below could be created by cutting a... (answered by ikleyn,Alan3354)
If a regular pentagon has a side of length 2X+1, what is the perimeter of the... (answered by stanbon)
if the perimeter of a pentagon is 60, its average size length... (answered by ewatrrr)
The side of a regular pentagon is 25 cm. If the radius of its inscribed circle is 15 cm,... (answered by Boreal,Alan3354,ikleyn)
The side of a regular pentagon is 25 cm. If the radius of its inscribed circle is 15 cm,... (answered by ikleyn)
A regular pentagon has sides of 20 cm. An inner pentagon with sides of 10 cm is inside... (answered by MathLover1)