you are giving MOM trouble again! ~_*
Since DAE' = 1/2 B, DAB = 1/2 A thus,
BAE' = DAE' + DAB = 1/2 (A+B) > 1/2 (B+B) = B
Since DAE' = 1/2 B, DAB = 1/2 A thus,
BAE' = DAE' + DAB = 1/2 (A+B) > 1/2 (B+B) = B