
06218054
j
2013f.00509
Pritchard, Chris
Generalizing complementary regions.
Math. Sch. (Leicester) 42, No. 2, 1113 (2013).
2013
Mathematical Association (MA), Leicester
EN
G43
E53
elementary geometry
plane geometry
quadrilaterals
area
triangles
parallelograms
trapeziums
trapezoids
kites
diagonals
geometry software
Anne\rq s theorem
vector products
conjectures
proofs
ME 2013f.00508
From the introduction: In the previous article [the author, ibid. 42, No. 1, 1011 (2013; ME 2013f.00508)] we found that if a point is placed arbitrarily inside a rectangle, and that point joined to all four vertices to create four regions, then opposite, complementary regions have the same total area. Does this property hold for any other shapes? How about the parallelogram, the trapezium, the kite or indeed the general quadrilateral?