Generalizing Van Aubel' Theorems. Level: High School, College geometry

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If similar rhombi with centers E, F, G and H are constructed externally on the sides of quadrilateral ABCD as shown in illustration above, then:

1.Segments EG and FH are congruent.

2. The angle of EG and FH equals the angle of the sides of the rhombi.

3. If K, L, M, and N are the midpoints of the segments A'A", B'B", C'C", and D'D", then LN and KM lie on perpendicular lines.

4. The ratio of JL and KM equals the ratio of the diagonals of the rhombi.

 

Source:
For generalizations of Van Aubel's theorem (and associated generalizations for triangles when two vertices coincide) go to:

Dual Generalizations of Van Aubel's Theorem by Michael de Villiers and
Generalizing Van Aubel: Michael de Villiers' Theorems.

 

See also:

 Van Aubel's Theorem. Quadrilateral with Squares. Proof with animation.

 
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Last updated: October 27, 2007