“微信扫一扫”进入题库练习及模拟考试
初中数学八年级下册（648题）
如图，在四边形
知识点：第十八章 平行四边形
参考答案：证明：\(\because AC\)是\(BD\)的垂直平分线，点\(F\)在\(AC\)上，
\(\therefore AB = AD\)，\(BC = CD\)，\(FD=FB\)，
\(\because \)在\(\Delta ABF\)和\(\Delta ADF\)中，
\(\left\{ {\begin{array}{*{20}{l}} {AB = AD} \\ {FB = FD} \\ {AF = AF} \end{array}} \right.\)，
\(\therefore \Delta ABF \cong \Delta ADF({\rm{SSS}})\)，
\(\therefore \angle ABF = \angle ADF\)，\(∠BAC=∠DAC\)
\(\because \angle BEC = \angle ADF\)，
\(\therefore \angle BEC = \angle ABF\)，
\(\therefore AB//CD\)，
\(\therefore \angle BAC = \angle ACD\)，
\(\therefore \angle DAC = \angle ACD\)，
\(\therefore AD = CD\)，
\(\because AB = AD\)，\(BC = CD\)，
\(\therefore AB = CB = CD = AD\)，
\(\therefore \)四边形\(ABCD\)是菱形。