given the regular polygon, select all of the rotations and reflections that carry the figure onto itself.

A. A rotation of 72º around the center, point D.

C. A reflection across line b through one vertex, the center d.

E. A reflection across line c, and the midpoint of the opposite side

Step-by-step explanation:

From Euclidean Geometry we get that sum of internal angles inside a polygon equals 360º and there is the following relationship in regular polygons:

(Eq. 1)

Where:

- Internal angle, measured in sexagesimal degrees.

- Number of sides, measured in centimeters.

If we know that , then internal angle of regular pentagon is:

In consequence, rotating the regular pentagon 72º around the pentagon carries the figure onto itself due to angular symmetry. (Correct A)

By adding any line passing the center of the regular pentagon (i.e. line cc', line bb'), which is collinear to any vertex and any point of the figure, we guarantee conditions of length symmetry so that reflection carries the figure onto itself. (Correct answers: C, E)