M is the middle point of BC side in triangle ABC, DM is vertical to em, D and E are on AB and AC respectively, connecting De, proving that De is less than BD = CE

M is the middle point of BC side in triangle ABC, DM is vertical to em, D and E are on AB and AC respectively, connecting De, proving that De is less than BD = CE

Extend DM to f so that DM = MF
CF, EF,
△BDM≌△CFM,(S,A,S),
∴BD=CF.
EM is the vertical bisector of DF, de = EF
In △ CEF, EF < EC + CF,
That is, de < BD + EC