初中数学八年级上册试题库（555题）

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已知∠AOB＝30°，点P在∠AOB的内部，P₁与P关于OA对称，P₂与P关于OB对称，

判定\(△{P}_{1}O{P}_{2}\)的形状。

知识点：第十三章　轴对称

参考答案：\(\because {P_1}\)与\(P\)关于\(OB\)对称\(\therefore OP = O{P_1}\)，\(\angle {P_1}OB = BOP\)\(\because {P_2}\)与\(P\)关于\(OA\)对称\(\therefore OP = O{P_2}\)，\(\angle {P_2}OA = AOP\)\(\therefore O{P_1} = O{P_2}\)，\(\angle {P_1}O{P_2} = 2\angle BOA = 60^\circ \)\(\therefore \)△\({P_1}O{P_2}\)为等边三角形