Geometry Puzzle: Cut The Figure to Make Two Identical Parts

[bob012345]

Here is a little puzzle from Pierre Berloquin’s book 100 Geometric Games. The goal is to cut the figure once to make two identical parts. Have fun!

 

[kuruman]

Does "identical" mean that after the object is cut into two, one can superimpose the two pieces into one with no more than a simple rotation in the plane of the screen?

 

[bob012345]

Does "identical" mean that after the object is cut into two, one can superimpose the two pieces into one with no more than a simple rotation in the plane of the screen?

Identical here means they have the same shape. Think of it like two pieces of physical paper. Only the shapes matter.

 

[kuruman]

Identical here means they have the same shape. Think of it like two pieces of physical paper. Only the shapes matter.

This doesn't help. A cut along the red line produces two pieces that have the same shape, namely rectangles. Is this a valid solution? If not, why not?

 

[FactChecker]

Identical here means they have the same shape. Think of it like two pieces of physical paper. Only the shapes matter.

Can you flip one, so that a clockwise outer perimeter becomes a counter-clockwise perimeter?