Determine whether a regular decagon has reflection symmetry and/or rotational symmetry. If it
has reflection symmetry, state the number of axes of symmetry. If it has rotation symmetry,
state the angle of rotation. Explain how you determined your answers
To determine whether a regular decagon has reflection symmetry, we need to examine if it can be reflected over a line so that the reflected shape matches the original decagon.
For a regular decagon, we know that all sides are equal in length and all angles are equal, measuring 144 degrees.
To determine if it has reflection symmetry, we would look for axes of symmetry. An axis of symmetry is a line that divides an object into two mirror-image halves.
In the case of a regular decagon, there are a total of 10 axes of symmetry. Each axis would pass through one vertex of the decagon and the midpoint of the opposite side.
Therefore, a regular decagon has reflection symmetry with 10 axes of symmetry.
To determine if a regular decagon has rotational symmetry, we need to check if it can be rotated by a certain angle and still look the same.
In this case, since a regular decagon has 10 sides, it can be rotated by 36 degrees, which is the equivalent of one-tenth of a full circle, and still maintain its shape.
Therefore, a regular decagon has rotation symmetry with an angle of rotation of 36 degrees.
In summary:
- A regular decagon has reflection symmetry with 10 axes of symmetry.
- A regular decagon has rotation symmetry with an angle of rotation of 36 degrees.