题目:已知:如图,四边形ABCD是平行四边形,PQ是对角线BD上的两点,且BP=DQ,求证:AP和QC互相平行且相等。(北师大版九年级上册第三章习题)图1简证:由题中已知条件,易证△APD≌△CQB(或△DQC≌△BPA),结论即可成立。引申一,由于四边形ABCD是平行四边形,而矩形、菱形、正方形都是特 Title: Known: As shown, the quadrangle ABCD is a parallelogram, PQ is two points on the diagonal BD, and BP = DQ. Verify that AP and QC are parallel and equal to each other. (Beijing Normal University Edition 9th grade book Chapter 3 exercises) Figure 1 Evidence: From the known conditions, easy to prove △APD ≌ △ △ CQB (or △ DQC ≌ △ △ BPA), the conclusion can be established. Extended one, since the quadrilateral ABCD is a parallelogram, rectangles, diamonds, and squares are all special