Thread: A proof regarding regular pentagons - help needed

ABCDE is a pentagon. Squares have been constructed on each of the 4 sides of this pentagon acting as a base. The centroid of each square has been determined and a pentagon constructed with these centre points as vertices as shown in the diagrom that is attached.

I would like to prove that given that the smaller pentagon ABCDE is REGULAR this implies the larger penatgon PQRST is also a regular pentagon. Can anyone help?

Originally Posted by marzi

ABCDE is a pentagon. Squares have been constructed on each of the 4 sides of this pentagon acting as a base. The centroid of each square has been determined and a pentagon constructed with these centre points as vertices as shown in the diagrom that is attached.

I would like to prove that given that the smaller pentagon ABCDE is REGULAR this implies the larger penatgon PQRST is also a regular pentagon. Can anyone help?

1. Don't post graphic attachments in word documents use an image file format
so we can see it without having to download the file.

2. Tell us under what rules you are required to prove this. The construction
has the same symmetries as the original regular pentagon so trivially the final
pentagon is regular.

RonL