初中数学八年级上册试题库（555题）

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如图，已知\(AB//CD\)，\(OA = OD\)，\(AE = DF\)．试说明：\( EB=CF\)。

知识点：第十二章　全等三角形

参考答案：证明：\(\because AB//CD\)，\(\therefore \angle 3 = \angle 4\)，在\(\Delta ABO\)和\(\Delta DCO\)中，\(\left\{ {\begin{array}{*{20}{l}}
{\angle 3 = \angle 4} \\
{OA = OD} \\
{\angle 1 = \angle 2}
\end{array}} \right.\)，\(\therefore \Delta ABO \cong \Delta DCO(ASA)\)，\(\therefore AB = CD\)，\(\because \angle 3 = \angle 4\)，\(\therefore \angle CDF = \angle BAE\)，在\(\Delta ABE\)和\(\Delta DCF\)中，\(\left\{ {\begin{array}{*{20}{l}}
{AE = DF} \\
{\angle BAE = \angle CDF} \\
{AB = CD}
\end{array}} \right.\)，\(\therefore \Delta ABE \cong \Delta DCF(SAS)\)，\( EB=CF\)。