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向量在高中数学教材中的教育价值不仅体现在它有利于培养学生数形结合的思想方法,有利于拓宽解题思路,有利于发展学生的运算能力,更重要的是它有利于与高等教育衔接.三角形与平面向量的交汇是高考新的题型,是高考的热点,借助向量工具重点考查正、余弦定理及三角形的面积公式,以及三角函数的图像和性质.解答这类问题要熟练向量数量积的运算法则和性质,注意方程思想方法的运用~([1]).本文在证明三角形垂心的性质的基础上~([2]),以三角形的边为基底,利用向量的基本定理,将垂心的性质拓宽到三角形四心.
The educational value of vector in high school mathematics textbooks is not only reflected in its ideological and method of cultivating students ’combination of numbers and forms, but also beneficial to broaden the way of solving problems and the development of students’ computing ability. More importantly, it is conducive to the connection with higher education Intersection of triangles and plane vectors is a new type of college entrance examination, is a hot spot in the college entrance examination, with the help of vector tools focus on positive and cosine theorem and the triangle area formula, as well as the triangular function of the image and nature of these questions to be skilled vector quantity ([1]). On the basis of proving the nature of the vertical centroid of the triangle, we use the basic theorem of the vector as the base of the triangle, Broken heart to the nature of the triangle four hearts.