### A square in parallel lines

An square intersects two parallel lines located at distance from each other. The points of intersection are cross joined. Prove that the angle so obtained is

The problem is credited to V. V. Proizvolov (Kvant 1996 (2)) and may serve an example where using dynamical software to sketch a diagram proves to be a distraction. I put together a GeoGebra applet and looked at the possible properties of the configuration with several elements added. Meanwhile, Hubert Shutrick pointed out its obvious, salient feature. The solution is a one liner.

### Solution

The angle formed by a transversal with two parallel lines is uniquely determined by its length between the lines - and vice versa.

The rest is easy:

[...] 题目来源： http://www.mathteacherctk.com/blog/2013/05/a-square-in-parallel-lines [...]

May 24th, 2013 at 9:46 am