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Theorems
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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.
