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第43頁

信息發(fā)布者：

解：相似

$∵?∠A=36°，??AB=AC?$

$∴?∠ABC=∠C=72°?$

$∵?BD?平分?∠ABC?$

$∴?∠ABD=∠CBD=36°?$

$∴?∠CBD=∠A，??∠C=∠C?$

$∴?△ABC∽△BCD?$

解：相似。

$∵??∠1=∠2??$

$∴??∠BAC=∠DAE??$

$∵??∠3=∠2，??三角形內(nèi)角和為??180，??對頂角相等，$

$∴??∠ACD=∠AED，??$

$由??∠BAC=∠DAE，????∠ACD=∠AED??$

$得??△ABC∽△ADE??$

$解：∵??∠ABC=∠ADC，????∠P=∠P??$

$∴??△BPC∽△DPA??$

$∴??\frac {PC}{PA}=\frac {BP}{DP}??$

$∵??PB=PA+AB=3+2=5??$

$∴??\frac {2}{3}=\frac {5}{DP}??$

$∴??DP=7.5??$

$∴??CD=PD-PC=5.5??$

$證明：∵??△ABC??是等邊三角形$

$∴??∠ABC =∠ACB= 60°，????AB= BC??$

$∵??AB= BC，????∠ABC =∠ACB，????BD= CE??$

$∴??△ABD≌△BCE??$

$∴??∠BAD=∠DBF??$

$又∵??∠ADB=∠BDF??$

$∴??△BDF∽△ADB??$

$??BD ：???? AD= DF：???? DB??$

$即??BD2=AD · DF??$

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