通过反射变换作轴对称图形是几何解题的一个重要方法。但在许多问题中,往往图形本身或其部分就具有对称性,只要我们善于发现并加以利用,就能给解题带来很大的方便。兹举数例如下: 例1 正三角形ABC内接于⊙○,D、E分别是AB、AC的中点,P在BC上,PD、PE分别交AB、AC于M、N,求证:M、O、N共线。连接OA、OM、ON,只须证∠AOM+∠AON=180°。注意到点O、D关于AB对称,点O、E Axisymmetric maps through reflection transformation are an important method of solving geometric problems. However, in many problems, the graph itself or its parts are often symmetrical. As long as we are good at discovering and using it, we can bring great convenience to the problem. For example, the following examples are given: Example 1 The positive triangle ABC is inscribed with ⊙○, D and E are the midpoints of AB and AC, P is on BC, and PD and PE are transmitted to AB and AC to M and N, respectively. , O, N collinear. Connecting OA, OM, and ON requires only AOM+∠AON=180°. Note points O, D about AB symmetry, points O, E