“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,在菱形\(ABCD\)中,点\(E\)\(F\)分别在\(BC\)\(CD\)上,连接\(AE\)\(AF\),且\(\angle BAE = \angle DAF\)求证:\(CE = CF\)

图片 38    



知识点:第十八章 平行四边形


参考答案:证明:\(\because \)四边形\(ABCD\)是菱形,\(\therefore AB = AD = BC = CD\),\(\angle B = \angle D\),在\(\Delta ABE\)和\(\Delta ADF\)中,\(\left\{ {\begin{array}{*{20}{l}}
{\angle BAE = \angle DAF} \\
{AB = AD} \\
{\angle B = \angle D}
\end{array}} \right.\),\(\therefore \Delta ABE \cong \Delta ADF(ASA)\),\(\therefore BE = DF\),\(\therefore BC - BE = CD - DF\),即\(CE = CF\)。

进入考试题库