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三角形中位线定理涉及到了线线平行、一条线段等于另一条线段之半以及等分线段等内容,在几何题中有着十分广泛的应用。一、当题设中有过同一点的两线段的中点连线段,但少第三边时,应设法添出第三边,构造出三角形,再运用定理。例1 如图1,在四边形ABCD中,E、F、G、H分别为AB、BC、CD、DA的中点,求证:四边形EFGH为平行四边形。
The triangle median line theorem involves the parallel lines, a line segment equal to half of the other line segment, and the contour line segment, which has a very wide range of applications in geometric problems. 1. When there is a middle point connecting line of two lines that have the same point in the title setting, but when there is less third edge, we should try to add the third edge, construct a triangle, and then use the theorem. Example 1 As shown in Figure 1, in the quadrilateral ABCD, E, F, G, and H are the midpoints of AB, BC, CD, and DA, respectively. Verify that the quadrilateral EFGH is a parallelogram.