在几何证明题中,有一类问题是要证明线段的和、差、倍、分关系,如何构造线段的和、差、倍、分,便成为解决此类问题的关键.这里通过两例,进行分析.例1如图1,在ΔABC中,AB=AC,点D为BC边上一点,过点D作DF⊥AB于点F,DE⊥AC于点E,过点C作CG⊥AB于点G.求证:DF+DE=CG.A C G F E BD图1%分析一要证明DF+DE=CG,就是要 In the proof of geometry problem, there is a kind of problem that is to prove the sum, difference, multiplication and division of line segments, and how to construct the sum, difference, multiplication and division of line segments becomes the key to solving such problems. Example 1 As shown in Fig. 1, in ΔABC, AB = AC, point D is a point on BC, point D for DF⊥AB at point F, point DE⊥AC at point E, point C for CG⊥AB at Point G. Proof: DF + DE = CG.ACGFE BD Figure 1% Analysis First to prove DF + DE = CG, is to