初中数学八年级下册（648题）

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知识点：第十八章　平行四边形

参考答案：证明：
\(\because BD\)平分\(\angle ABC\)，
\(\therefore \angle ABD = \angle CBD\)，
\(\because \)在\(\Delta ABD\)和\(\Delta CBD\)中\(\left\{ {\begin{array}{*{20}{l}}
{\angle ABD = \angle CBD} \\
{\angle A = \angle C} \\
{BD = BD}
\end{array}} \right.\)，
\(\therefore \Delta ABD≌\Delta CBD(AAS)\)，
\(\therefore AB = BC\)，\(AD = DC\)，
\(\because AB = AD\)，
\(\therefore AB = BC = DC = AD\)，
\(\therefore \)四边形\(ABCD\)是菱形。