2005年中考大幕已落,凸显新的课程标准的试题也比比皆是,聊城市的这道以平行四边形为载体,内有三个中点的试题,不失为一道重点考查的好题.题目已知:ABCD中,对角线AC、BD相交于点O,BD=2AD,E、F、G分别是OC、OD、AB的中点.求证:(1)BE⊥AC;(2)EG=EF.图1分析(1)由平行四边形的对边 The 2005 high school entrance exam has been closed, and the questions that highlight the new curriculum standards can be found everywhere. The Liaocheng city uses a parallelogram as its carrier. There are three midpoint questions in it. It is a good question to focus on. In ABCD, the diagonals AC and BD intersect at point O, BD=2AD, E, F, and G are the midpoints of OC, OD, and AB, respectively. Proof: (1) BE⊥AC; (2) EG=EF Fig. 1 Analysis (1) The opposite side of a parallelogram