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近年来中考中,出现了一类平行四边形折叠问题.解答时需注意:在折叠前后,折痕两边能够完全重合的部分是全等图形,它们的对应线段相等、对应角相等.现举例介绍如下:例1如图1,在平行四边形ABCD中,点E、F分别在边DC、AB上,DE=BF,把平行四边形ABCD沿直线EF折叠,使得点B、C分别落在B′、C′处,线段EC′与线段AF交于点G,连接DG、B′G.(1)求证:EG=FG;(2)DG=B′G吗?为什么?
In recent years, a series of parallelogram folding problems have appeared in the middle school entrance examination. When answering, it should be noted that before and after the folding, the parts where the creases are completely coincident are the congruent graphs. Their corresponding line segments are equal and the corresponding angles are equal. The following is an example. : Example 1 As shown in Fig. 1, in the parallelogram ABCD, points E and F are on the sides DC and AB, respectively, DE=BF, and the parallelogram ABCD is folded along the straight line EF so that the points B and C fall on B’ and C, respectively. ′′, the line segment EC′ intersects the line segment AF at point G, connecting DG, B′G. (1) Verification: EG=FG; (2) DG=B′G? Why?