近年来中考中,以重叠部分图形为背景的问题屡见不鲜.现仅以2012年的中考题为例介绍如下:例1(湖南省益阳市)如图1所示,在面积为3的正方形ABCD中,E、F分别是BC和CD边上的两点,AE⊥BF于点G,且BE=1.(1)求证:△ABE≌△BCF;(2)求出△ABE和△BCF重叠部分(即△BEG)的面积; In the middle school entrance examination in recent years, the overlapping part of the graphics for the background of the common problems are now only 2012 test questions as an example as follows: Example 1 (Hunan Province, Yiyang City) as shown in Figure 1, an area of ​​3 square ABCD , E and F are two points on the edge of BC and CD, respectively, AE⊥BF is at point G and BE = 1. (1) Verify: △ ABE≌ △ BCF; (2) Find the overlap between △ ABE and △ BCF (Ie △ BEG) area;