如图,在△ABC中,AB=BC=AC,DE⊥AB,DF⊥AC,请比较△AEF和四边形EBCF的周长的大小.
如图,在△ABC中,AB=BC=AC,DE⊥AB,DF⊥AC,请比较△AEF和四边形EBCF的周长的大小.
数学人气:659 ℃时间:2020-05-01 02:38:01
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∵AB=BC=AC,∴∠A=∠B=∠C=60°,∵DE⊥AB,DF⊥AC,∴∠BDE=∠FDC=30°,∴BE=12BD,CF=12CD,∴BE+CF=12(BD+CD)=12BC,∴BE+CF+BC=32BC,AE+AF=3BC−32BC=32BC,∴AE+AF+EF=BE+CF+BC+EF,∴△AEF和四边形EBCF的...
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