A line that bisects the right angle in a right triangle also bisects a square erected on the hypotenuse:

http://www.futilitycloset.com/wp-content/uploads/2011/09/2011-09-12-half-and-half-2.png

[as a new user, I can't embed the image directly]

source: http://www.futilitycloset.com/2011/09/12/half-and-half/