Question

如图,已知M为AB中点,EF平行AB,求证：CD平行AB

Answer 1

令AF、BE的交点为O.

∵EF∥AM,∴△CEF∽△CMA,∴EF/MA＝CE/CM.

∵EF∥MB,∴△DEF∽△DBM,∴EF/BM＝DF/DM.

∵MA＝BM,又EF/MA＝CE/CM、EF/BM＝DF/DM,∴CE/CM＝DF/DM,∴EF∥CD,又EF∥AB,

∴CD∥AB.