初中数学八年级上册试题库（555题）

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如图，∠MON=60°，点A在射线OM上，点B，C在射线ON上（点C在点B的右侧），且∠OAB+∠OAC=60°.点B关于直线OM的对称点为D，连接CD．用等式表示线段CD，AB之间的数量关系，并证明。

知识点：第十三章　轴对称

参考答案：\(CD = AB\)证明：连接\(AD\)，\(OD\)，\(\because \)点\(B\)关于直线\(OM\)的对称点为\(D\)，点\(A\)在射线\(OM\)上，\(\therefore AD = AB\)，\(\angle OAD = \angle OAB\)，\(\because \angle OAB + \angle OAC = 60^\circ \)，\(\therefore \angle OAD + \angle OAC = 60^\circ \)，即\(\angle DAC = 60^\circ \)，在\(\vartriangle OAC\)中，\(\angle ACO = 180^\circ - \angle OAC - \angle AOC = 180^\circ - (60^\circ - \angle OAB) - 60^\circ = 60^\circ + \angle OAB\)，又\(\because \angle ABC = \angle AOB + \angle OAB = 60^\circ + \angle OAB\)，\(\therefore \angle ACO = \angle ABC\)，\(\therefore AB = AC\)，\(\therefore AC = AD\)，又\(\because \angle CAD = 60^\circ \)，\(\therefore \vartriangle ACD\)是等边三角形，\(\therefore CD = AD\)，\(\therefore CD = AB\)．