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電子課本網(wǎng) 第46頁

第46頁

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$解:?(1)?如圖所示$
$?(2)∠A=∠A,??△ABC∽△A'B'C'?$
$在?AB?上截取?AB''= A'B',?過點(diǎn)?B''?作?B''C''//BC,?交?AC?于點(diǎn)?C''?$
$在?△ABC?和?△AB''C''?中$
$∵?B''C''//BC?$
$∴?△ABC \sim △AB''C''?$
$∴?\frac {AB}{AB''}=\frac {BC}{B''C''}=\frac {CA}{C''A}?$
$∵?\frac {AB}{A'B'}=\frac {BC}{B'C'}=\frac {CA}{C'A'},??AB''= A'B'?$
$∴?B''C''= B'C',??C''A= C'A',??△AB''C''≌△A'B'C'?$
$∴?△ABC \sim △A'B'C'?$
$?(3)?假設(shè)?AB>A'B',?在?AB?上截取?AB''= A'B',?過點(diǎn)?B''?作?B''C''//BC,?交?AC?于點(diǎn)?C''?$
$在?△ABC?和?△AB''C''?中$
$∵?B''C''//BC?$
$∴?△ABC \sim △AB''C''?$
$∴?\frac {AB}{AB''}=\frac {BC}{B''C''}=\frac {CA}{C''A}?$
$∵?\frac {AB}{A'B'}=\frac {BC}{B'C'}=\frac {CA}{C'A'},??AB''= A'B'?$
$∴?B''C''= B'C',??C''A= C'A',??△AB''C''≌△A'B'C'?$
$∴?△ABC \sim △A'B'C'?$
解:三邊成比例的兩個(gè)三角形相似
C
7.5
2
B