Which a regular octagon rotates 360° about its center. how many times does the image of the octagon coincide with the preimage during the rotation? will always map a parallelogram onto itself?

The word you are looking for is rotational symmetry and for that an octagon has orders of 8 (that is what you call the times it overlaps) I do not know what you mean on the swcong question

Step-by-step explanation:

A way of finding out how many orders a shape has of rotational symmetry is by getting some tracing paper and tracing the shape. You then put your pencil on the center of the shape and count how many time the shape overlaps

8 times
because the sides of the octagon are all equal so as it rotates from the center it coincides with the preimage 

8 times

Step-by-step explanation:

By definition, the sum of the exterior angles of a polygon is 360 degrees.

Therefore, each exterior angle of the polygon is:

Where n is the number of sides of the polygon.

 The lengths of the sides of  a regular octagon are equal and the measures of the internal angles are equal too.

The sum of the exterior angles of a polygon is 360 degrees and it has 8 sides, therefore, the measure of each exterior angle is:

You know that the regular octagon rotates 360° about its center.

Therefore, keeping all the above on mind, you have that the number of times (which you can call x) the image of the octagon coincide with the preimage during the rotation is:

8 times

Step-by-step explanation:

An octagon has eight sides of equal length and eight angles of same measure. So, If it is rotated 360 degrees about its center. It would coincide with all of its 8 sides. So, it will coincide with it's pre-image 8 times.

8

Step-by-step explanation:

Step-by-step explanation:

because A regular octagon is a closed figure with sides of the same length and internal angles of the same size. so if it is rotated 360 degrees it should coincide with its preimage after every 45 degrees.

so 360/45= 8 times

A regular octagon has 8 sides, so it would coincide exactly each time the vertices fall into the same places. In one full 360-degree rotation, any "selected" vertex would fall into all 7 other vertices one after the other, before going back to its original position. Therefore, there would be 8 times during the rotation that the octagon coincides with the preimage.

A regular octagon is a closed figure with sides of the same length and internal angles of the same size. so if it is rotated 360 degrees it should coincide with its preimage after every 45 degrees. So 360/45= 8 times

An octagon has 8 sides, a rotation of 45° (360°/8) will map the octagon onto its preimage. Answer is 8.

Given that the octagon rotates 360 degrees, it is a given that for every regular division of the polygon (360/8 = 45 degrees), the image would coincide with the pre-image during the rotation. Therefore, the octagon would coincide a total of 8 times as it rotates 360 degrees about its center.