初中数学八年级上册试题库（555题）

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如图，在\(\Delta ABC\)和\(\Delta ADE\)中，\(AB = AE\)，\(AB//ED\)，\(\angle DAB = \angle BAE + \angle B\)．

求证：\(AC = ED\)。

知识点：第十二章　全等三角形

参考答案：证明：\(\because AB//ED\)，\(\therefore \angle EAB = \angle E\)，\(\because \angle DAB = \angle BAE + \angle B\)，\(\angle DAB = \angle BAE + \angle DAE\)，\(\therefore \angle B = \angle DAE\)，在\(\Delta ABC\)和\(\Delta EAD\)中，\(\left\{ {\begin{array}{*{20}{l}}
{\angle B = \angle DAE} \\
{AB = EA} \\
{\angle BAC = \angle E}
\end{array}} \right.\)，\(\therefore \Delta ABC \cong \Delta EAD(ASA)\)，\(\therefore AC = ED\)．