Triangle ABC paper with a yellow front and blue back is shown in Figure 1. This paper is folded as shown in Figure 2 such that vertex B comes onto vertex A.
Accordingly, which of the following is the correct ordering of the lengths $|\mathrm{AC}|$, $|\mathrm{AE}|$, and $|\mathrm{BD}|$?
A) $|\mathrm{AC}| < |\mathrm{AE}| < |\mathrm{BD}|$
B) $|\mathrm{AC}| < |\mathrm{BD}| < |\mathrm{AE}|$
C) $|\mathrm{AE}| < |\mathrm{AC}| < |\mathrm{BD}|$
D) $|\mathrm{AE}| < |\mathrm{BD}| < |\mathrm{AC}|$
E) $|\mathrm{BD}| < |\mathrm{AE}| < |\mathrm{AC}|$