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数学思想是数学的生命和灵魂,是解决数学问题的根本策略.下面我们运用数学思想攻克一些平面图形中的典型问题.一、转化思想例1如图1,求∠A+∠B+∠C+∠D+∠E+∠F+∠G的度数.【解析】方法一:如图2,这七个角可以转化到△AGN、四边形BCDM和四边形EFNM中,∠A+∠G=∠1,∠B+∠C+∠D+∠2=360°,∠E+∠F+∠1+∠3=360°,又∠2+∠3=180°,所以∠A+∠B+∠C+∠D+∠E+∠F+∠G=360°+360°-180°=540°.
Mathematical thinking is the life and soul of mathematics, is the fundamental strategy to solve mathematical problems. Below we use mathematical thinking to overcome some of the typical problems in the plane graphics .A conversion thought example 1 as shown in Figure 1, ∠A + ∠B + ∠C + ∠D +解E + ∠F + ∠G degrees. 【Method】: As shown in Figure 2, these seven corners can be transformed into △ AGN, quadrilateral BCDM and quadrilateral EFNM, ∠A + ∠G = ∠1, ∠B + ∠C + ∠D + ∠2 = 360 °, ∠E + ∠F + ∠1 + ∠3 = 360 ° and ∠2 + ∠3 = 180 °, so ∠A + ∠B + ∠C + ∠D + ∠E + ∠F + ∠G = 360 ° + 360 ° -180 ° = 540 °.