如图,在正方形ABCD中,F为DC的中点,E为BC上的一点,且EC=1/4BC,那么AF垂直EF.

CE=1/4*BC
BE=3/4*BC
AF^2=AD^2+DF^2=AD^2+1/4*CD^2=5/4*AD^2
EF^2=EC^2+FC^2=1/16*BC^2+1/4*DC^2=5/16*AD^2
AC^2=AB^2+BE^2=AB^2+9/16*BC^2=25/16*AD^2
AE^2=25/16*AD^2=20/16*AD^2+5/16*AD^2=EF^2+AF^2
即：AE^2=AF^2+EF^2 ,所以AF垂直EF.