初中数学八年级上册试题库（555题）

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如图：已知\(BD = CD\)，\(BF \bot AC\)，\(CE \bot AB\)，求证：点\(D\)在\(\angle BAC\)的平分线上。

知识点：第十二章　全等三角形

参考答案：\(\because BF \bot AC\)，\(CE \bot AB\)，\(\therefore \angle BED = \angle CFD = 90^\circ \)，在\(\Delta BED\)和\(\Delta CFD\)中，\(\left\{ {\begin{array}{*{20}{l}}
{\angle BED = \angle CFD} \\
{\angle BDE = \angle CDF} \\
{BD = CD}
\end{array}} \right.\)，\(\therefore \Delta BED \cong \Delta CFD(AAS)\)，\(\therefore DE = DF\)，又\(\because DE \bot AB\)，\(DF \bot AC\)，\(\therefore \)点\(D\)在\(\angle BAC\)的平分线上．