In the triangle ABC, D is the midpoint of AB, points E and F are on AC and BC respectively, and the triangle DEF is less than or equal to the triangle ade + BDF

In the triangle ABC, D is the midpoint of AB, points E and F are on AC and BC respectively, and the triangle DEF is less than or equal to the triangle ade + BDF

From EF, De, DF is the middle line of triangle ABC
So EF / / AB, DF / / AC, de / / BC, so, according to the parallelogram rule, triangle def = ade = DFB
So it must be smaller than that

As shown in the figure, points D, e and F are the midpoint of each side of the triangle ABC respectively. It is proved that the triangle ade, triangle BDF, triangle CEF and triangle def are congruent

As shown in the picture
∵ D, e and F are the midpoint of each side of the triangle ABC
The three median lines of triangle are de, EF and DF
∴df‖bc,de‖ac,ef‖ab
∴df=be=ce,de=af=cf,ef=ad=bd
≌ ade ≌ BDF ≌ CEF ≌ def (SSS congruent)