平行四边形的性质有其特殊性,应用广泛.它与三角形、四边形、梯形等存在着广泛的联系.有关平行四边形的证题颇多,现略举数例. 例1 如图1,△ABC的AC边上的三等分点顺次为G、H,AB、BC的中点分别为E、F,连结EG、FH并延长交于D.连结AD、DC,求证:四边形ABCD是平行四边形. The nature of the parallelogram has its own particularity and is widely used. It has extensive connections with triangles, quadrilaterals, trapezoids, etc. There are many questions about parallelograms. Here are a few examples. Example 1 As shown in Figure 1, △ABC The three equally divided points on the AC side are G, H, respectively. The midpoints of AB and BC are E and F respectively. Connect EG and FH and extend it to D. Connect AD and DC. Prove that the quadrilateral ABCD is a parallelogram.