Proof of folding to trisect a right angle

Question

If first you fold a normal (letter or A4) piece of paper in half:

and then you fold one corner to meet the halfway line:

Then you've trisected the right angle at bottom left - but how does one prove this?

Answer 1

The left side, the folded left side and the reflection of the folded left side at the halfway line together form an isolateral triangle, of which the fold line is an angular bisector.

Answer 2

We wrote out a proof in our book, Geometric Folding Algorithms: Linkages, Origami, Polyhedra:

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