An Ingenious Dudeney Dissection This problem will show how to dissect the regular heptagon...

An Ingenious Dudeney Dissection This problem will show how to dissect the regular heptagon (seven-sided polygon) to form a square.

(a) The figure below shows a dissection of the heptagon to form a parallelogram. Point C is located on a diagonal so that AB = AC, AL = LD, and NE = NF; L, M, and N are midpoints on their respective segments. It follows that the triangles labeled 1 and 2, 5, and 12 are similar isosceles triangles having angle measures 77 1/7°, 77 1/7°, and 25 5/7° respectively. Verify this, and complete your explanation of how the pieces formed will make a parallelogram.

(b) The square dissection of a parallelogram (discussed earlier) is superimposed onto the preceding dissection. Complete these details and provide your own explanation of the desired dissection of the given heptagon.

DISSECTION OF REGULAR HEPTAGON TO FORM A SQUARE