[alogo] Lines of segments

Given are two parallel lines a, b and two points on each: (A,A1) and (B,B1) respectively. For any real number x, construct the points Ax = (1-x)*A + x*A1, Bx = (1-x)*B + x*B1. The segment AxBx depends on x, and has the following properties.
[1] AAx/AxA1 = BBx/BxB1 for every x.
[2] Lines Lx = AxBx pass through the intersection point C of AB and A1B1.
[3] AxBx/BxC is constant i.e. independent of x.

[0_0] [0_1] [0_2]
[1_0] [1_1] [1_2]

All properties are trivial consequences of Thale's theorem. The figure here is a preamble to the much more interesting figure, resulting by retaining all definitions except the parallelity of lines a and b. This is studied in LinesOfSegments2.html .

See Also


Return to Gallery

Produced with EucliDraw©