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平行四边形是最常见的特殊四边形之一,利用其对边、对角及对角线的特殊关系可以解决许多几何问题．特别地,当题目中涉及中点、中线或中位线时,要多考虑构造平行四边形来帮助解题．例1 如图1,梯形ABCD中,AB// CD,M、N分别是AB、CD的中点．DE// BC交AB于E,DF//MN交AB于F．求证：EF=1/2(AB-CD)．分析：由已知,可知四边形 BCDE和四边形 MNDF均是平行四边形,从而 CD=BE,MF=DN．又因M、N分别是
Parallelograms are one of the most common special quadrilaterals. Many geometric problems can be solved by using the special relations between the sides, diagonals and diagonals. In particular, when the title involves midpoint, midline or median line, consider constructing a parallelogram to help solve the problem. Example 1 As shown in Figure 1, in the ABCD ladder, AB/CD, M, and N are the midpoints of AB and CD, respectively. DE// BC pay AB to E, DF//MN AB to F. Proof: EF = 1/2 (AB-CD). Analysis: It is known that the quadrilateral BCDE and the quadrilateral MNDF are all parallelograms, and CD=BE and MF=DN. And because M and N are