Chapter 14.8, Problem 23WE

a.

To determine

To draw the figure if there is one that meets the conditions.

Answer to Problem 23WE

The figure ofan octagon with eight rotational symmetries.

  

Explanation of Solution

Given information:

The given condition is that a parallelogram with four symmetry lines.

The figure ofan octagon with eight rotational symmetries.

  

The above figure is of regular octagon which has eight rotational symmetries. It has all eight sides equal and all angles are also equal. Four lines about which the figure has rotational symmetry connects the opposite corners and other four are which bisects opposite sides.

b.

To determine

To draw the figure if there is one that meets the conditions.

Answer to Problem 23WE

The figure ofan octagon with four rotational symmetries.

  

Explanation of Solution

Given information:

The given condition is that a parallelogram with just two symmetry lines.

The figure ofan octagon with four rotational symmetries.

  

The above figure is of octagon which has four rotational symmetries. It has all eight angles equal but all sides are not equal. Four lines about which the figure has rotational symmetry connects the opposite corners.

c.

To determine

To draw the figure if there is one that meets the conditions.

Answer to Problem 23WE

The figure of an octagon with only point symmetry.

  

Explanation of Solution

Given information:

The given condition is that a parallelogram with just one symmetry line.

  

The above figure is of an octagon with only point symmetry. The above octagon is a non-regular octagon and the opposite sides are parallel.