Rhombus Angle Quadrisection Result

What do you notice about the quadrilateral EFGH formed by the quadrisectors of the angles of a rhombus ABCD? (Note: the quadrisectors divide the angles into four equal parts.)

Drag points A, B or C to dynamically change the figure. Click on the Button to display the measured lengths of the sides of the formed figure. What you notice?

Rhombus Angle Quadrisection Result

Conjecture: Though it is easy to see (and prove) from symmetry that the quadrilateral formed by dividing the angles of a rhombus into n equal parts is generally a rectangle, we see in this case, where the angles are divided into four equal parts, that a special rectangle, namely, a square, is formed.

Challenge: Can you logically explain (prove) this observation?

Only if stuck, go to Rhombus Angle Quadrisection Proof).

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Created by Michael de Villiers, 25 April 2011; updated 19 April 2021.