Henry Ernest Dudeney/Modern Puzzles/122 - Folding a Pentagon/Solution

Modern Puzzles by Henry Ernest Dudeney: $122$

If you are given a perfectly square piece of paper,

how are you going to fold it so as to indicate by creases a regular pentagon,

all ready to be cut out?

Take the square $\Box ABCD$.

Fold $\Box ABCD$ in half horizontally so $A$ lies on $B$ to get the midpoint $E$ of $AB$.

Fold $EC$.

Fold $EF$ to make $B$ lie on $EC$ at $G$.

Fold $CB$ onto $CE$ to make $H$ lie on $G$.

Fold $AB$ at $K$ to make $B$ lie on $H$.

Fold $\Box ABCD$ in half vertically along $PQ$ so as to make $K$ lie on $L$.

$BC$ is now said to be divided in medial section.

$KL$ is one of the sides of the regular pentagon.

Fold at $K$ so that $L$ lies on $AB$ at $M$.

Fold at $L$ so that $K$ lies on $CD$ at $N$.

Fold at $M$ so that $K$ lies on $PQ$ at $O$.

We can also fold at $N$ so that $L$ also lies on $PQ$ at $O$.

Folding $KM$, $LN$, $MO$ and $NO$ completes the construction.