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在三角形和四边形的已知条件中,含有中点的问题是一种常见题型.对于这类问题.联想到三角形(或梯形)的中位线或直角三角形斜边上的中线的性质,若设法找到另一个与待证结论关联的中点作连线,往往可使解题思路豁然开朗.例1如图1,在四边形ABCD中,AD=BC,M、N分别是BD、AC的中点,直线MN分别交BC、AD于F、E.求证:∠AEF=∠BFE.分析注意到已知条件中有两个中点M和N,联想到三角形中
In the known conditions of triangles and quadrilaterals, the problem of containing the midpoint is a common type of problem. For such problems, the nature of the median line on the hypotenuse of a triangle (or trapezoid) Trying to find another connection to the midpoint associated with the conclusions to be witnessed can often lead to a solution to the problem. Example 1 As shown in Figure 1, in a quadrilateral ABCD, AD = BC, M, N are BD, AC Point, line MN respectively pay BC, AD in F, E. Proof: ∠ AEF = ∠ BFE. Analysis noted that there are two known midpoints M and N, associated with the triangle