Henry Ernest Dudeney/Puzzles and Curious Problems/191 - Two Squares in One/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $191$

Two squares of any relative size can be cut into $5$ pieces, in the manner shown below,

that will fit together and form a larger square.

But this involves cutting the smaller square.

Can you show an easy method of doing it without in any way cutting the smaller square?

Place the two squares together so that $AB$ and $CD$ are straight lines.

Locate the centre point of the larger square.

Draw $AD$

Draw $EF$ and $GH$ through that centre point parallel to and perpendicular to $AD$ respectively.

Then you can cut out pieces $1$, $2$, $3$ and $4$, which, together with the smaller square $5$, fit together to form the big square of side $AD$.

This dissection was discovered by Henry Perigal in about $1830$, and published by him in $1873$.