2. It is easy to prove △ AMB △ DMB by extending AM and CB to D, and get AB=DB. Extending AN and BC to e also gives AC=EC. MN is the median line in △ADE, so MN=(a+b+c)/2.

3. Intercept CE=CD on CA and connect DE. Prove △ DCB △ DEA, and then draw a conclusion.

4. I can't see this topic clearly

5. extend FD to g so that DG=DF, connect BG, and connect GE and EF.

Yi Zheng △ FDC △ GDB

From △AEB∽△AFC, EA/AF=EB/FC=EB/BG is obtained.

And ∠ EAF = 360-∠ EAB-∠ FAC-∠ BAC = ∠ EBC+∠ FCB = ∠ EBC+∠ GBC = ∠ EBG.

So △EAF∽△EBG

So ∠FEA=∠BEG

So ∠ Feg = ∠ AEB = 90.

And ED is the center line of △FEG, so ED=FG/2=DF.