This animation is based on a section of the book, Illustrated Special Relativity Through Its Paradoxes, by John de Pillis and Jose' Wudka.
GIVEN: A swivel point lies L units along a straight line that forms angle θ with the vertical. Another line swivels through this point and intersects the two 45o lines.
THEN: The swiveling line is bisected exactly when its angle with the horizontal is also θ. Moreover, L (described in the paragraph above) is equal to the lengths of the two lines resulting from the bisection of the swiveling line.