Question 50
A piece of paper is the square $ABCD$. We fold it by placing the vertex $D$ on the point $D'$ of the side $BC$. We assume that $AD$ moves on the segment $A'D'$, and that $A'D'$ intersects $AB$ at $E$. Prove that the perimeter of the triangle $EBD'$ is one half of the perimeter of the square.