How to cut an irregular shape into 2 congruent parts

Question

Is it possible to cut this shape:

into 2 congruent parts (equal area and shape).

The guy who gave us this teaser said that it's possible. But i can't for the life of me figure out how.

In the figure, $ABCD$ is a square, angle $CDE$ is a right angle, and the curve $AE$ is a circular arc with center $C$.

Do you mean to divide it into two equal parts with a single straight line? — Intelligenti pauca, Mar 28 '18 at 22:26
Doesn't have to be a straight line. Any single cut from one side to another that divides it into 2 congruent shapes will do. — kuke, Mar 28 '18 at 22:40

score 4 · Accepted Answer · answered Mar 28 '18 at 22:49

4

(This space intentionally left blank.)

answered Mar 28 '18 at 22:49

Blue

1

Ah, i can't believe i didn't look at it like that yet... it has rotational symmetry. Thank you very much! – kuke Mar 28 '18 at 23:22
What software did you use to make this image? – orlp Mar 28 '18 at 23:28
1

@orlp: GeoGebra – Blue Mar 28 '18 at 23:30

1 Answers1