变换是极为重要的数学思维方法,利用几何变换解题在数学竞赛中经常用到,本讲介始几何变换中的基本变换:轴对称及中心对称变换、平移及旋转变换。 一、轴对称变换 把一个图形F沿着一直线l折过来,如果它能够与另一个图形F′重合,我们就说图形F和F′关于这条直线l对称。 两个图形中的对应点叫做关于这条直线l的对称点,这条直线l叫做对称轴,如右图。 轴对称图形有以下两条性质: Transformation is an extremely important mathematical thinking method. The use of geometric transformation to solve problems is often used in mathematical competitions. This lecture introduces basic transformations in geometric transformations: axisymmetrical and centrally symmetrical transformations, translational and rotational transformations. First, the axisymmetric transformation A graphic F is folded along a straight line l, if it can coincide with another graphic F’, we say that the graphics F and F ’is symmetrical about this line l. The corresponding point in the two graphs is called the symmetry point about this line l. This line l is called the symmetry axis, as shown in the right figure. Axisymmetric graphs have the following two properties: