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歡迎您訪問數學考題練習:如圖,?ABCD中,對角線AC和BD相交于點O!

數學考題練習:如圖,?ABCD中,對角線AC和BD相交于點O

更新時間:2024-01-12 16:25:23作者:貝語網校

如圖,?ABCD中,對角線AC和BD相交于點O,△AOB的周長為15,AB=6,求對角線AC與BD的和是多少?

試題答案

解:∵四邊形ABCD是平行四邊形,

∴AC=2AO,BD=2BO,

∵△AOB的周長為15,AB=6,

∴AB+OA+OB=15,

∴AO+OB=15-6=9,

∴AC+BD=2(AO+OB)=2×9=18.

試題解析

根據平行四邊形性質得出AC=2AO,BD=2BO,根據△AOB的周長和AB求出AO+OB,即可求出答案.

點評:本題考查了平行四邊形性質,注意:平行四邊形的對角線互相平分.

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