In my previous post Golden Rectangles in a Right Triangle I constructed three golden rectangles in the right-angled triangle with sides of length 3, 4, and 5. I continue this construction by drawing lines through existing points, then marking new points at the intersections of perpendicular lines. This results in two more golden rectangles being identified, these each being flush with one of the perpendicular sides of the triangle and with each other. Their dimensions are 1 x φ and 2 x 2/φ, where φ is the golden ratio. They are shaded in the diagram. A trigonometric proof by Ed Staples shows that φ is indeed key to this construction.
