Let be ∆ABC in which D and E are the mid points of AB and AC respectivily. BC parrallel to DE. in triangle ADE draw the two perpendicular on AD and AE. And D point meet with C and point E meet with B . And DM and NE are the two perpendicular on side AE And AD respectively.In ∆ADE, Ar ∆ ADE = 1/2 X AD X NE. (1)AND, AR ∆ ADE= 1/2 X AE X MD (2) And in AR. ∆ BCD = 1/2 X NE X BD (3) IN AR. ∆ DCE = 1/2 X MD X EC. (4) FROM 1 and 3AR ∆ ADE = AD_________________AR. ∆ BCD = BD. FR0M 2and 4AR.∆ ADE = AE________________Ar. ∆ DCE = EC. Ar.∆ BCD = Ar∆ DCE. (Both triangles lie on same base and parallel lines)AR. ∆ ADE. AR.∆ ADE___________ Equals to (=)____________Ar. ∆BCD. AR.∆ BCEHence, AD. AE ____. = ______ BD. CE
By BPT theorem.