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1．如图1,在◇ABCD中,对角线相交于点 O．MN//AC,交AB于点M,交BC于点N．连接 AN．问：和△ADM等面积的三角形有几个？ 2．如图2是一个长、宽、高分别为6、4、3的长方体木块．一只蚂蚁要从长方体木块的一个顶点A处,沿着长方体的表面爬到和A相对的顶点B处吃食物．试分析它需要爬行的最短路线并计算最短路线的长． 3．如图3,在Rt△ABC中,∠ACB=90°,BC的垂直平分线DE交BC于D,交AB于E,F在 DE的延长线上,并且AF=CE． (1)求证：四边形ACEF是平行四边形．
1. As shown in Figure 1, in ◇ABCD, the diagonal lines intersect at the point O. MN//AC, AB at point M, and BC at point N. Connect AN. Q: How many triangles are there, such as △ ADM? 2. Figure 2 is a rectangular parallelepiped with length, width and height of 6, 4 and 3, respectively. An ant climbs from one of the vertices A of the rectangular wood block and climbs along the surface of the box to eat food at the vertex B opposite to A. Try to analyze the shortest route it needs to crawl and calculate the length of the shortest route. 3. In Figure 3, in Rt △ ABC, ∠ ACB = 90°, and the vertical bisector of BC intersects BC in D, AB in E, F in DE, and AF = CE. (1) Proof: Quadrilateral ACEF is a parallelogram.