一到希望杯试题 As shown in the figure 25,in△ABC we have AB=BC=CA,DF⊥AC,DE⊥AB.Please compare themagnitudes of the perimeter of △AEF and the perimeter of quadrilataral EBCF中文大意: 在正△ABC中 AB=BC=CA,BC上有一点D,DE⊥AB,
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一到希望杯试题
As shown in the figure 25,in△ABC we have AB=BC=CA,DF⊥AC,DE⊥AB.Please compare themagnitudes of the perimeter of △AEF and the perimeter of quadrilataral EBCF
中文大意: 在正△ABC中 AB=BC=CA,BC上有一点D,DE⊥AB,DF⊥AC.试比较三角形AEF和四边形EBCF的周长
因为AB=BC=CA,且ED⊥AB,DF⊥AC,则∠EDB=∠FDC=30°,所以BD=2BE,DC=2FC,则四边形BCFE=EF+BE+FC+BD+DC=3BE+3FC+EF,
而C△AEF=AE+EF+AF=AB-BE+AC-FC+EF=2BC-BE-FC+EF=2(BD+DC)-BE-FC+EF=3BE+3FC+EF.
所以三角形AEF和四边形EBCF的周长相等
一到希望杯试题 As shown in the figure 25,in△ABC we have AB=BC=CA,DF⊥AC,DE⊥AB.Please compare themagnitudes of the perimeter of △AEF and the perimeter of quadrilataral EBCF中文大意: 在正△ABC中 AB=BC=CA,BC上有一点D,DE⊥AB,
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