题目内容
如图,在正方形网格上有△ABC和△DEF.
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(1)求证:△ABC∽△DEF;
(2)计算这两个三角形的周长比;
(3)根据上面的计算结果,你有何猜想?
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(1)求证:△ABC∽△DEF;
(2)计算这两个三角形的周长比;
(3)根据上面的计算结果,你有何猜想?
(1)证明见解析;(2)1:2;(3)周长比等于相似比.
试题分析:(1)根据网格得出两三角形的各边长度,进而根据各边的比值得出对应边的关系;
(2)利用网格求出两三角形周长即可;
(3)根据(2)中计算,即可猜想周长与相似比的关系.
试题解析:∵AC=
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∴
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∴△ABC∽△DEF;
(2)∵
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∴△ABC的周长是2+
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∵DE=4 DF=2
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∴△DEF的周长是2(2+
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∴这两个三角形的周长比为:1:2;
(3)根据上面的计算结果可得出:周长比等于相似比.
考点: 相似三角形的判定与性质.
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