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用坐标法证明几何图形的性质,思路单纯,几乎无须添设辅助线,即使问题较为复杂,若坐标系选择恰当,运用此法亦常奏效.而坐标变换是解析几何的重要内容.作为这一方法的补充,本文举例说明平面直角坐标系的坐标变换公式在几何证明中的应用. 例1 六边形ABCDEF内接于⊙O,它的三边AB、CD和EF都等于圆的半径,M、N和P分别为边BC、DE和FA的中点.求证:△MNP为等边三角形.
Using the coordinate method to prove the nature of the geometry, the idea is simple, almost no need to add auxiliary lines, even if the problem is more complex, if the coordinate system is properly selected, this method is also often effective. The coordinate transformation is an important part of the analytical geometry. As this To complement the method, this paper illustrates the application of the coordinate transformation formula of the plane rectangular coordinate system to the geometrical proof. Example 1 The hexagon ABCDEF is inscribed in ⊙O, and its three sides AB, CD and EF are equal to the radius of the circle, M , N, and P are the midpoints of the edges BC, DE, and FA, respectively. Proof: △MNP is an equilateral triangle.