joining the middles of the parallel sides.

2) On EF lies also the intersection point H of the diagonals of the trapezium.

3) Points {E,F,H,G} form a harmonic tetrad (or division see Harmonic.html ).

Last property holds also for general quadrangles (see Quadrangle_0.html ).

1) Draw the medial line GE of the triangle GDC and show that it is also medial to triangle GAB.

2) Use Ceva's theorem (see Ceva.html ).

3) HE/HF = DE/FB, GE/GF = DE/AF etc.

In the file ParallelMedians.html we discuss an application of the previous properties to triangles.

d

2) It is also [Rouche, p. 330]:

(d

To prove (1) write the four following equations combine them to eliminate cosines and divide

the result by (a+b):

To show the second property do a similar calculation using triangles AHD and BHC,

setting AH = kd

d and c [Rouche, p. 335].

Combine the two equations of section-2 involving also {a,b} to find these lengths. Then

construct the trapezium knowing {a,b,c,d,d

Some additional properties of trapezia are discussed in the files Trapezium.html , Trapezium2.html .

Quadrangle_0.html

Ceva.html

ParallelMedians.html

Trapezium.html

Trapezium2.html

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