Question

如圖所示，點(diǎn)P為∠AOB內(nèi)一點(diǎn)，分別作出P點(diǎn)關(guān)于OA、OB的對(duì)稱(chēng)點(diǎn)P₁，P₂，連接P₁P₂交OA于M，交OB于N，P₁P₂=15，則△PMN的周長(zhǎng)為__________．

Answer 1

15．

【考點(diǎn)】軸對(duì)稱(chēng)的性質(zhì)．

【分析】P點(diǎn)關(guān)于OA的對(duì)稱(chēng)是點(diǎn)P₁，P點(diǎn)關(guān)于OB的對(duì)稱(chēng)點(diǎn)P₂，故有PM=P₁M，PN=P₂N．

【解答】解：∵P點(diǎn)關(guān)于OA的對(duì)稱(chēng)是點(diǎn)P₁，P點(diǎn)關(guān)于OB的對(duì)稱(chēng)點(diǎn)P₂，

∴PM=P₁M，PN=P₂N．

∴△PMN的周長(zhǎng)為PM+PN+MN=MN+P₁M+P₂N=P₁P₂=15．

故答案為：15

【點(diǎn)評(píng)】本題考查軸對(duì)稱(chēng)的性質(zhì)．對(duì)應(yīng)點(diǎn)的連線(xiàn)與對(duì)稱(chēng)軸的位置關(guān)系是互相垂直，對(duì)應(yīng)點(diǎn)所連的線(xiàn)段被對(duì)稱(chēng)軸垂直平分，對(duì)稱(chēng)軸上的任何一點(diǎn)到兩個(gè)對(duì)應(yīng)點(diǎn)之間的距離相等，對(duì)應(yīng)的角、線(xiàn)段都相等．